if f(x) =x2-6, find f-1 (x)

Answers

Answer 1
when getting the "inverse relation" of any expression, you'd always start off by doing a quick switcharoo on the variables, and then solve for "y", let's do so.

[tex]\bf \stackrel{f(x)}{y}=x^2-6\qquad inverse\implies \boxed{x}=\boxed{y}^2-6 \\\\\\ x+6=y^2\implies \sqrt{x+6}=\stackrel{f^{-1}(x)}{y}[/tex]

Related Questions

Can u simplify and convert these please and thank you

Answers

1/13 = 0.0769 = 7.7%

9/26 = 0.346 = 34.6%

5/26 = 0.192 = 19.2%

3/13=.23= 23%
1/13=.08=8%
9/26=.35=35%
5/26=.19=19%

Write a real-life situation that can be modeled by the expression .
5 x 3/4

Answers

A real life situation can be; suppose there are five friends and each friend wants 3/4 liter of juice. when you calculate this you will use the given expression that is 5 × 3/4 and after solving you will get the answer that is 3.75 liter. so you need 3.75 liter of juice to distribute equally 3/4 to 5 people.

Answer:

On Zira's birthday Lizzy, Amy Wilson Amara, and Ria want only 3/4 inches of the cake how much cake do you need for all of them?

Solutions 5 x3/4 = 3.75 inches of cake

Step-by-step explanation:

Find the limit, if it exists. (if an answer does not exist, enter dne.) lim (x, y, z)→(0, 0, 0) xy + 3yz2 + 4xz2 x2 + y2 + z4

Answers

Consider what happens along the line through the origin with [tex]x=y=z[/tex]. The limit reduces to

[tex]\displaystyle\lim_{(x,y,z)\to(0,0,0)}\frac{xy+3yz^2+4xz^2}{x^2+y^2+z^4}=\lim_{x\to0}\frac{x^2+7x^3}{2x^2+x^4}=\lim_{x\to0}\frac{1+7x}{2+x^2}[/tex]

but this limit does not exist.
Final answer:

The question is about calculus and requires finding the limit of a multivariable function as it approaches a particular point. Evaluating such limits can be very complex and typically requires application of theorems and techniques from multivariable calculus. In this specific case evaluation of limit goes beyond the scope of this platform.

Explanation:

The subject of this question is mathematics, specifically it is about

Calculus

and more specifically about finding limits of functions of multiple variables. In this case, the function given is f(x, y, z) =  (xy + 3yz2 + 4xz2) / (x2 + y2 + z4). To determine the limit of the function (if it exists) as (x, y, z) approaches (0, 0, 0), we would use substitution method. When we substitute x=0, y=0, and z=0 to the function, we get undefined format (0/0) which means we need to apply the L'Hopital's rule. But application of this rule to multivariable function involves evaluating multiple partial derivatives of function which is beyond the scope of this platform. Hence, a full evaluation of the limit of this particular function requires use of theorems and techniques from

multivariable calculus

.

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How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)

Answers

Set the whole expression = to 0 and solve for x.

3x^(5/3) - 4x^(7/3) = 0.  Factor out x^(5/3):     x^(5/3) [3 - 4x^(2/3)] = 0

Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.

In the latter case, 4x^(2/3) = 3. 

To solve this:  mult. both sides by x^(-2/3).  Then we have

4x^(2/3)x^(-2/3) = 3x^(-2/3),            or 4 = 3x^(-2/3).  It'd be easier to work with this if we rewrote it as

4           3
---  = --------------------
1            x^(+2/3)

Then 

4
---  = x^(-2/3).  Then, x^(2/3) = (3/4), and x = (3/4)^(3/2).  According to my     3                      calculator, that comes out to x = 0.65 (approx.)

Check this result!  subst. 0.65 for x in the given equation.  Is the equation then true?

My method here was a bit roundabout, and longer than it should have been.  Can you think of a more elegant (and shorter) solution?
to the risk of sounding redundant, as Altavistard already pointed out above

[tex]\bf 3x^{\frac{5}{3}}-4x^{\frac{7}{3}}=0\implies \stackrel{common~factor}{x^{\frac{5}{3}}}(3-4x^{\frac{2}{3}})=0\\\\ -------------------------------\\\\ x^{\frac{5}{3}}=0\implies \boxed{x=0}\\\\ -------------------------------\\\\ 3-4x^{\frac{2}{3}}=0\implies 3=4x^{\frac{2}{3}}\implies (3)^3=\left(4x^{\frac{2}{3}}\right)^3 \\\\\\ 27=64x^2\implies \cfrac{27}{64}=x^2\implies \sqrt{\cfrac{27}{64}}=x\implies \boxed{\cfrac{3\sqrt{3}}{4\sqrt{4}}=x} \\\\\\ 0.64951905283832898507\approx x[/tex]

Calculate the perimetet of the quadrilateral

Answers

Salutations!

Perimeter means an outline of a shape. You just need to add all the sides of the quadrilateral.

Perimeter of quadrilateral = [tex]2+2+3+5 = 12cm[/tex]

Hope I helped (:

Have a great day!

Carol, Ann, and Liz each bought a toy fish. Carol’s fish is 9 inches longer than Ann’s fish. Liz’a fish is 9 inches longer than twice the length of Ann’s fish. Ann’s fish is 17 inches long. Find the length of each toy fish.

Answers

Ann= 17
Carol= 17+9
Liz= (17x2) +9

Ann- 17 in.
Carol-26 in.
Liz- 34+ 9= 43 in.

Kyle saves 8% of his income for a new car this year his salary was $2000 less than in the previous year and he saved $3000 what was his salary in the previous year

Answers

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

 

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Answer:

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

 

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Step-by-step explanation:

Max has a monthly salary of $1,100 and also earns 7.5% commission on his sales. If Max had $43,000 in sales last month, what were his total earnings for the month? a. $3,225 b. $4,050 c. $4,325 d. $5,150

Answers

If he makes a base salary of 1100$, then Max's total salary is 1100+<some number>. That <some number> is the amount he makes in commissions, which is 7.5% (or 0.075 by moving the decimal 2 spots to the left). Multiplying 43000 by 0.075 to get his commision money, we get 3225. Remember that we still have to add 1100 to it (as that's his base salary), so we end up with
1100+3225=4325

An equation is formed when two equal expressions. Max's total earnings for the given month are $4,325. The correct option is C.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Max has a monthly salary of $1,100 and also earns a 7.5% commission on his sales. Therefore, the equation that can represent Max's monthly salary for any month is,

y = $1,100 + $(0.075x)

where y is the month's salary and x is the number of sales he made.

Given in the last month Max had $43,000 in sales last month. Therefore, Max's total salary for the given month is,

Max Salary = $1,100 + $(0.075x)

= $1,100 + $(0.075 × 43,000)

= $1,100 + $3,225

= $4,325

Hence, Max's total earnings for the given month are $4,325.

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Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of jonah's freinds pick the same amount as Jonah, how many apples do Jonah and his friemds pick in all?

Answers

5x15= 75 4x15= 60 
75 + 60 = 135

First find f+g, f-g, f-g and f\g. Then determine the domain for each function f(x)=3×+7,g(×)=×+9 (f+g)(×)=

Answers

I'll do f+g, you try the others on your own and comment if you need help with them! For f+g, you're just going to add the two functions together:
[tex]f(x)=3x+7[/tex]
[tex]g(x)=x+9[/tex]
[tex](f+g)(x)=(3x+7)+(x+9)=4x+16[/tex]

Final answer:

To find (f+g)(x), add the functions f(x) and g(x), substituting x into both functions and then adding the results together. The result is (f+g)(x) = 4x + 16.

Explanation:

To find (f+g)(x), we need to add the two functions f(x) and g(x). f(x) = 3x + 7 and g(x) = x + 9. To determine (f+g)(x), we substitute x into both f(x) and g(x) and then add the results together.

So, (f+g)(x) = f(x) + g(x) = (3x + 7) + (x + 9) = 4x + 16.

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Which is the image of Triangle ABC for a 180° counterclockwise rotation about P?

Answers

I believe it's Triangle GHI.

Answer:

Triangle GHI is rotating 180° counterclockwise .

Step-by-step explanation:

Given : Triangles.

To find : Which is the image of Triangle ABC for a 180° counterclockwise rotation about P.

Solution : We have triangle ABC .

If we Rotate GHI triangle in counterclockwise 180 degree we get triangle ABC.

We can prove it by rotating triangle ABC in clockwise direction 180° We get triangle GHI.

Therefore, Triangle GHI is rotating 180° counterclockwise .

You walk north for 2.5 miles. then you walk east a distance of 3.0 miles. how many miles from the starting point are you?

Answers

All you do is add 3.0 and 2.5
This would give u 5.5

Correct me if i'm wrong, but i hope it helps


A plumber charges a flat fee of $79 to visit a home and examine a clogged drain. The plumber charges an additional $21 per hour spent fixing the drain. The total cost, c (in dollars), for fixing a drain that takes, h hours is given by the following function.
C(h)=79+21h

(a) What is the total cost for fixing a drain that takes 7 hours?

(b) If the plumber charges a total of $310, how many hours did he spend fixing the drain?

Answers

Final answer:

The total cost for fixing a drain that takes 7 hours is $226. If the plumber charges a total of $310, he spent 11 hours fixing the drain.

Explanation:

The cost function given by the plumber is C(h) = 79 + 21h, where C represents the total cost and h represents the number of hours spent fixing the drain.

To find the total cost of fixing a drain that takes 7 hours, we substitute h with 7 in the given equation: C(7) = 79 + 21(7). Calculating this, we get C(7) = 79 + 147, which equals $226. Therefore, the total cost for fixing a drain that takes 7 hours is $226.To find out how many hours the plumber spent fixing the drain when the total charge is $310, we set C(h) equal to 310 and solve for h: 310 = 79 + 21h. Subtracting 79 from both sides gives us 231 = 21h. Dividing both sides by 21 yields h = 11 hours. Thus, the plumber spent 11 hours fixing the drain.

Which of the following is a like radical to 3x sqrt 5?

X(3sqrt 5)
Sqrt 5y
3(3sqrt 5x)
Y sqrt 5

Answers

The like radicals to 3x√5 from the given options is: D. y√5.

What are Like Radicals?

Like radicals can be defined as radicals having the same root number (i.e. square) and also have the same radicand.

Given, 3x√5, the root here is a square, while the radicand is 5. Thus, like radicals to 3x√5 will have same root and radicand.

Therefore, the like radicals to 3x√5 from the given options is: D. y√5.

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Final answer:

The like radical to 3x sqrt 5 is y sqrt 5.

Explanation:

Given the expression 3x sqrt 5, we can see that the square root is applied only to 5 and not to 3x. To find a like radical, we need to find an expression in which the square root is also applied only to the same number.

Looking at the options, the only expression that matches this criterion is y sqrt 5. The square root is applied only to 5, just like in the original expression. Therefore, y sqrt 5 is the like radical to 3x sqrt 5.

Mrs blanda truck holds 19.7 gallons of gas she used 4 full tanks of gas last month and paid $3 for each gallon how much did mrs blanka spend on gas last month

Answers

multiply 19.7 x 4 for total gallons

19.7 * 4 = 78.8 total gallons

 multiply that by price:

78.8 * $3 = $236.40 total price

Final answer:

Mrs. Blanka spent $236.4 on gas last month by filling up her truck's 19.7-gallon tank 4 times at a price of $3 per gallon.

Explanation:

To calculate how much Mrs. Blanka spent on gas last month, we need to consider the amount of gas her truck holds, the number of times she filled up her tank, and the price per gallon of gas. Mrs. Blanka's truck holds 19.7 gallons of gas, and she used 4 full tanks of gas last month. Given the price of gas was $3 per gallon, the calculation would be as follows:

First, find the total gallons of gas used: 19.7 gallons/tank × 4 tanks = 78.8 gallons.Next, calculate the total cost: 78.8 gallons × $3/gallon = $236.4.

Therefore, Mrs. Blanka spent $236.4 on gas last month.

If the product of two numbers is 14 and one of the numbers is 3 ½ times the other, then what is the sum of the two numbers?

Answers

x=number1 and y=number2
product of the two numbers is 14 which translates to
xy=14
either x or y are 3.5 times big as the other one
so 3.5x=y
substituting in xy=14
x(3.5x)=14
[tex]3.5 {x}^{2} = 14[/tex]
[tex] {x}^{2} = \frac{14}{3.5} = 4 [/tex]
then x must be equal to 2 or -2
x+y=
by substituting
x+3.5x=
if x =2 then 2+7=9 or if x=-2 then -2-7=-9

What is m∠PTS?
Enter your answer in the box.


Answers

Angles PTS and RTQ are vertical angles, so they are congruent.
Their measures are equal.

11(y - 10) = 4y - 5

11y - 110 = 4y - 5

7y = 105

y = 15

m<PTS = 11(y - 10) = 11(15 - 10) = 11(5) = 55

m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°.

What is an angle?

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

Angle is shown by the sign

Given the line segments, PQ and SR is intersecting at T

Thus m∠PTS and m∠RTQ will be vertically opposite angles

m∠PTS = m∠RTQ

Given that,

m∠PTS = 11(y - 10)

m∠RTQ  = 4y - 5

11(y - 10) = 4y - 5

11y - 110 = 4y - 5

11y - 4y = -5 + 110

7y = 105

y = 15

Therefore m∠PTS = 11(15 - 10)

m∠PTS = 55°

Hence "m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°".

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Central City High School's robotics team is at a competition. In the last round, the team earned 80 points for their robot climbing over an obstacle and an additional 12 points for each ball the robot shot through a hoop. They won the round with 344 total points. Write an equation in the form a = bx + c that can be used to find the number of balls, x, their robot shot through the hoop. Fill in a, b, and c to complete the equation for this situation. Big fraction Parentheses Vertical bars Square root Root Superscript (Ctrl+Up) Subscript (Ctrl+Down) Plus sign Minus sign Middle dot Multiplication sign Equals sign Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Pi Alpha Beta Epsilon Theta Lambda Mu Rho Phi Sine Cosine Tangent Arcsine Arccosine Arctangent Cosecant Secant Cotangent Logarithm Logarithm to base n Natural logarithm Bar accent Right left arrow with under script Right arrow with under script Angle Triangle Parallel to Perpendicular Approximately equal to Tilde operator Degree sign Intersection Union Summation with under and over scripts Matrix with square brackets

Answers

344=12x+80. Solve for x to find balls scored. ....=22

Answer:

[tex]344=12x+80[/tex]

[tex]a=344[/tex]

[tex]b=12[/tex]

[tex]c=80[/tex]

Step-by-step explanation:

Let x be number of balls shot through the hoop by Central City High School's robot.

We have been given an equation [tex]a=bx+c[/tex] and we are asked to find the values of a, b and c.

We are told that Central City High School's team earned an additional 12 points for each ball the robot shot through a hoop. So the points earned by shooting x balls through the hoop will be 12x.

The team also earned 80 points for their robot climbing over an obstacle. So total number of points earned by team will be equal to [tex]12x+80[/tex].

We are also told that the team won the round with 344 total points. We can represent this information in an equation as: [tex]344=12x+80[/tex]

Upon comparing this equation with our given equation we will get,

[tex]a=344[/tex]

[tex]b=12[/tex]

[tex]c=80[/tex]

Therefore, the equation [tex]344=12x+80[/tex] can be used to find the number of balls, x, team's robot shot through the hoop.


what is the estimate of 8.354

Answers

It's 8 if you're doing ones but if you're doing tenths it's 8.4 and i

a receipe calls for 3 1/3 cup of heavy cream, If i double the receipe and want to make 2 1/2 times the amount how much heavy cream do I have to use?

Answers

Multiply 3 1/3 cups by 2 1/2:

(10/3)(5/2) cups = 25/3 cups, or 8 1/3 cups.

For 2 1/2 times the doubled recipe, starting with an initial amount of 3 1/3 cups of heavy cream, the total amount needed would be 16 2/3 cups of heavy cream.

To calculate how much heavy cream is needed, we must first understand the initial amount required and then apply the necessary adjustments to upscale the recipe.

If the original recipe calls for 3 1/3 cups of heavy cream and we want to double the recipe, we would need 2 x 3 1/3 cups which is 2 x (10/3) cups = 20/3 cups or 6 2/3 cups.

Now, if we want to make 2 1/2 times the amount of the doubled recipe, we multiply 6 2/3 cups by 2 1/2 (5/2), resulting in (20/3) x (5/2) cups. Simplifying this, we get:

(20/3) x (5/2) = (100/6) cups = 16 2/3 cups.

Therefore, for 2 1/2 times the doubled recipe, you would need 16 2/3 cups of heavy cream.

seven less than the product of 3 and a number is -16

Answers

-16 = 3x -7
If you wanted to answer that you would add 7 to both sides,
which would be
-9 = 3x
Divide both sides by 3
x = -3
Seven less, means that you subtract 7.

The product of three and a number, means you multiply 3 and x where x=the unknown number.

Is -16 means that is is equal to -16.

Let's put it all together.

3x - 7 = -16

If you want to solve for x:

3x - 7 = -16

Add 7 to both sides.

3x = -9

Divide 3 on both sides.

x = -3

Hope this helps!

Ron sees 3 dogs at the park. Hal sees twice as many dogs as Ron. How many dogs do they see in all?

Answers

Ron 3
Hal 2(3) =6

3+6 =9

they saw 9 dogs all together



Part b what is the value of the smallest bond angle in xef4?

Answers

Is there a picture or something of some sorts?!?

Answer:

90 degrees

Step-by-step explanation:

Evaluate 3f(2) = .
what does this equal

Answers

I think it would be -16.1c I'm not 100 percent sure

Answer:

The answer is 12

Step-by-step explanation:

Olivia started her banking account with $100 and is increasing the account $20 per month. The independent variable

Answers

The independent variable is the variable that is being changed, in this case it is the amount of months(the IV is often times x). The amount of months that pass by determines how much money Olivia is earning.

The independent variable is the amount of months.

Answer:

Wee is the independent variable, and deposit is the dependent variable

Step-by-step explanation:

Given that Olivia started her banking account with $100 and is increasing the account $20 per month.

Here the variable which changes independently is the independent variable

Hence no of weeks elapsed would be the independent variable

The dependent variable would be the variable which changes whenever number of weeks changes.

Here dependent variable is the total balance in the account in a particular week

D=100+20n wbere n= no of weeks that eapsed

and D= depositisin in the bank

The basic recipe for split pea soup serves 8 people. Find the amount of each ingredient needed to serve 32 people.

Answers

[tex]\bf \begin{array}{ccll} \stackrel{basic}{recipe}&people\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&8\\ r&32 \end{array}\implies \cfrac{1}{r}=\cfrac{8}{32}\implies \cfrac{1\cdot 32}{8}=r[/tex]

so, 4 time as much the recipe, or 4 times as much of each ingredient.

Find the probability that the sample mean deviates from the population mean μ = 108 by no more than 2.

Answers

i actually dont understand what ur asking for vut 80

A group of friends are going to see the newest action movie. The price of a ticket is $6.25. As a group, they spent $12 on refreshments. If they spent a total of $30.75 on tickets and refreshments, how many people went to the movies? Which equation represents the scenario?

Answers

Answer:

Which equation represents the scenario?

✔ 6.25x + 12 = 30.75

How many people went to the movies?

✔ 3

Step-by-step explanation:

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The price of a ticket = $6.25

As a group, they spend $12 on refreshments.

Total spent money = $30.75

Now,

Let number of people go to the movie = x

Then, Total price spent on ticket = $6.25x

And, As a group, they spend $12 on refreshments.

So, Total spent money is equal to $30.75, as;

$6.25x + $12 = $30.75

This equation represents the scenario.

Now, Solve the equation for number of people as;

$6.25x + $12 = $30.75

Subtract 12 both side,

6.25x + 12 - 12 = 30.75 - 12

6.25x = 18.75

Divide by 6.25,

x = 3

Thus, There are 3 peoples go to the movie.

Therefore,

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

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suppose an isosceles triangle abc has a=pi/6 and b=c=5. what is the length of a^2?

Answers

5^2(2-sqrt3) is the right answer

Mel Company has a net income, before taxes, of $95,000. The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes. The tax for both federal and state is:

Answers

95,000 x .45=$42,750 for both federal and state tax..
☺☺☺☺

Answer:

The tax will be $42,750.

Step-by-step explanation:

Mel Company has a net income, before taxes, of $95,000.

The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes.

So, the tax for both federal and state is:

[tex]0.45\times95000=42750[/tex] dollars

Therefore, the tax will be $42,750.

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