If f(x)=square root of 2-x and g(x)=x-1, then find the domain of h(x)=f(x)/g(x)

Answers

Answer 1

Let's examine what the conditions on the domains of f and g have to be before we examine h. Since f is defined:

[tex]f(x)= \sqrt{2-x} [/tex], we know that the function will be undefined when 2 - x < 0, or when x > 2, so we have the restriction on our domain that x ≥ 0.

g(x) has no such restrictions and is defined for all possible values of x, so its domain is all real numbers, or [tex]\mathbb{R}[/tex].

Since h(x) is a rational function, we know that it's undefined when its denominator is 0. In this case, our denominator is g(x), so the function is undefined when g(x)=0. x - 1 = 0 only when x = 1, so the second restriction on our domain for h is that x ≠ 1. Putting those two together, we find that the domain of h(x) is all values of x ≥ 0, where x ≠ 1.

Answer 2

Answer:

Domain of h(x) : [2,∞)

Step-by-step explanation:

Given: Two functions

[tex]f(x)=\sqrt{2-x}[/tex]

[tex]g(x)=x-1[/tex]

Composite function, [tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]

[tex]f(x)=\sqrt{2-x}[/tex], It is square root function. As we know square root function is always greater than 0.

2-x ≥ 0

2 ≥ x

Domain of f(x) : [2,∞)

[tex]g(x)=x-1[/tex], It is straight line equation (Linear function) As we know domain of linear function is all real number.

Domain of g(x) : (-∞,∞)

[tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]

[tex]h(x)=\dfrac{\sqrt{2-x}}{x-1}[/tex] , It is rational function. Denominator can't be zero.

So, x-1 ≠ 0

x ≠ 1

Now, we will see domain of h(x) common all three domain.

Domain of h(x): [2,∞)

Hence, The domain of h(x) is [2,∞)

Related Questions

How long should the metal stripping be to protect the edge of circular table top if the radius of the top is 2 feet

A) 1.26 feet
B) 4 feet
C) 122 feet
D) 6.28
E) none

Answers

The answer is B) 4 feet, common sense.

find factors of 14y^2+41y+15

Answers

(7y + 3) • (2y + 5) im not sure it's that answer ☺

the costume designer decides to make the sashes a little smaller, so that each of the 8 dresses can have a sash. What fraction of fabric should the costume maker use to make each sash

Answers

The costume designer should use 1/8 of the fabric dedicated to sashes for each dress.

Final answer:

The fraction that the costume maker should use for each sash is 1/8 of the total fabric available, as the fabric is being evenly divided among the 8 dresses.

Explanation:

If the costume designer is making sashes for 8 dresses and aims to use each bit of fabric equally, then each sash should consist of 1/8 of the total fabric. This is because the total fabric is being divided evenly among the 8 dresses. For example, if the costume designer has 8 yards of fabric, then each sash would use 1 yard of fabric (8 divided by 8 equals 1).

In fraction terms, each sash uses 1/8 of the fabric available. So for each dress, the costume designer should use 1/8 of the total fabric to make a sash.

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6 people share 3/5 pounds of peanuts equally what fraction of a pound of peanuts does each person receive

Answers

Hello! To solve this problem, we have to do 3/5 / 6, because you are dividing 3/5 of a bag among six people. In other words, it would be 3/5 * 1/6. You keep the first fraction, change the division sign into a multiplication one, and flip 6 into 1/6. 3/5 * 1/6 = 3/30 or 1/10 in simplest form. Each person receives 1/10 of a pound of peanuts.

The function y_p(t) = \ln(1 + 2 t), \ t > -\frac{1}{2}, is a particular solution to the differential equation y^{\,\prime\prime} + 3 y = g(t). find g(t)

Answers

The given particular solution is
[tex]y_{p}(t) = ln(1 + 2t) - \frac{1}{2} [/tex]

The ODE is
y'' + 3y = g(t)

Obtain the derivatives of the particular solution.
[tex]y_{p}^{'} = \frac{2}{1+2t} \\\\ y_{p}^{''} = \frac{-4}{(1+2t)^{2}} [/tex]

Because the particular solution should satisfy the ODE, therefore

[tex]g(t)=- \frac{4}{(1+2t)^{2}} +3 \, ln(1+2t)- \frac{3}{2} [/tex]

Answer: [tex]g(t) = - \frac{4}{(1+2t)^{2}} + 3 \, ln(1+2t) - \frac{3}{2} [/tex]

Given that [tex]y_{p(t)}=\ln{(1+2t)}, \ \ \ t\ \textgreater \ -\frac{1}{2} [/tex] is a particular solution to the differential equation [tex]y^{\prime\prime}+3y=g(t)[/tex]

Then

[tex][\ln{(1+2t)}]^{\prime\prime}+3[\ln{(1+2t)}]=g(t) \\ \\ \Rightarrow\bold{g(t)= \frac{2(1+6t)}{(1+2t)^2}+3\ln{(1+2t)}}[/tex]

What is the volume of a 575 gram bar of pure gold

Answers

19.32=density D=m÷v so, v=m÷d
v=575÷19.32 v=about 29.8

The length of a rectangle is five times its width. If the area of the rectangle is 125 m2 , find its perimeter.

Answers

It is 125 divided by 5

L = length
W = width

L = 5W ---- Length is 5 times the width
A = LW= 125

first lets find L and W

A = LW = 125-----LW is the formula for area of a rectangle
we know L = 5W
we'll plug in 5W for L
A = (5W)W = 125
A = 5W^2 = 125
W^2 = 125/5
W^2 = 25
Take the squareroot
W = 5

L = 5W
L = 5 * 5
L = 25

P = Perimeter = 2(L + w) ----- formula for perimeter of a rectangle
P = 2(25 + 5)
P = 60

bird leaves its nest and travels 18 miles per hour downwind for x hours. On the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours. What is the distance of the entire trip?

Answers

d = distance down wind
d - 6 = distance back
time = distance ÷ speed
x = d/20
x = (d - 6)/(16)

so d/20 = (d - 6)/16. Cross multiply
20d - 120 = 16d
-120 = -4d
30 = d so the whole trip assuming the bird gets back to the starting point is 60 miles

An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum values of I

Answers

Final answer:

The maximum value of the electric current I is 1 + √8, and the minimum value is -1 - √8, found by considering the amplitudes of the cosine and sine components in the given function.

Explanation:

The maximum and minimum values of an electric current, I, can be found by analyzing the function I=cos(wt)+√8sin(wt), where w is a constant and ≠0.

To find the maximum and minimum values, we need to consider the amplitude of the sine and cosine components separately. The maximum amplitude of the cosine function is 1, and for the square root of 8 times the sine function, it is √8. Therefore, the maximum possible value of the current is when both the sine and cosine functions are at their peaks. In this case, the maximum value of I would be 1 + √8.

To find the minimum value, we consider the case when the cosine function is at its minimum value, -1, and the sine function is also at its minimum, which can also be - √8. Therefore, the minimum possible value of I would be -1 - √8.

Rewrite the expression 2(1+2)-9 using the distributive property.

Answers

2(1+2) - 9 =

2 + 4 - 9 =

6 - 9 =

-3

this is using the distributive property and not using the 'correct' way

hope this helps

How many solutions does 25-4x=15-3x+10-x have

Answers

25 - 4x = 15 - 2x + 10
-10 - 10
15 - 4x = 15 - 2x
-15 -15
-4x = - 2x
no solution

Answer: The given equation will have infinite number of solutions.

Step-by-step explanation: We are given to check the number of solutions to the following equation :

[tex]25-4x=15-3x+10-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the number of solutions, we must solve the given equation.

The solution of equation (i) is

[tex]25-4x=15-3x+10-x\\\\\Rightarrow 25-4x=25-4x\\\\\Rightarrow 4x-4x=25-25\\\\\Rightarrow 0=0,[/tex] which is always true.

Thus, the given equation will have infinite number of solutions.

if you had a fraction strip folded into twelfths what fractional lengths could you measure with the strip

Answers

You could use inches to measure

Line l passes through the origin and point (3,4).What is the slope of a line parallel to line l

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{ 3}}\quad ,&{{ 4}})\\ &origin \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{4-0}{3-0}\implies \cfrac{4}{3}[/tex]

so, that's the slope of a line passing through the origin and 3,4, and any line parallel to it, will have the same exact slope.

How to find the least common denominator of 10x/x-3 and 4x/x-2

Answers

You multiply the denominators I believe

I mean obviously u.s prices are cheaper but is it really better? I need help

Answers

no because quality over quantity as you wouldn't want a hat for $14 that could easily break when if you paid a dollar more it would be more long lasting

you have 5 quarts of paint. It takes 5/8 quarts to paint each chair you are asked to paint. How many chairs can you paint?

Answers

You can pain 8 chairs; (5/8*8=5)

Can someone show me how to do this pleases?!.

solve the equation.

- 2 = 3x/5 + 1

Answers

1. -2=1/2x

2.1/2x=-2

3. 2*(1/2x)=(2)*(-2)

4. x=-4

Hope this helps :)

-2=1/2x

1/2x=-2

2*(1/2x)=(2)*(-2)

x=-4

I hope this helped! :)

the picture shows a barn door what is the distance BC between two horizontal parallel bars?

Answers

We know the lenght of the side adjacent to angle A, AC, and we want to know the opposite side, BC. What trig ratio describes the relationship between opposite and adjacent? The Tangent!

tan (x) = opp / adj
In this case, tan (45°) = BC / 4
To get BC by itself, multiply both sides by 4
4 * tan (45°) = BC

The answer is D

evaluate the function

can someone please explain how I would solve this please?

Answers

y = 4 x 2^-6
y = 4 x 1/2^6
y = 4 x 1/64
y = 1/16

To think intuitively of what it means to take a number to a negative power, first consider how we define taking a number to a positive power.

Before we even get there, though, consider how we define multiplication as repeated addition. When you see an expression like 3 x 5, what that essentially translates to is "add 3 to itself 5 times," so we could also write 3 x 5 as 3 + 3 + 3 + 3 + 3. Having established that, around middle school, you'll typically get your first exposure to positive exponents, which are defined at first as repeated multiplication. When you see something like [tex]3^5[/tex], we could also read that as "multiply 3 by itself 5 times," or [tex]3\times3\times3\times3\times3[/tex].

With that definition for positive exponents defined, it makes sense that we would define negative exponents in terms of the inverse of repeated multiplication: repeated division. Each time we step the exponent back by 1, we divide by the base again. For example, let's take these decreasing powers of 3 and notice what happens:

[tex]3^3 = 27\\3^2=27/3=9\\3^1=9/3=3\\3^0=3/3=1[/tex]

If we start stepping back further, we start getting to values below 1:

[tex]3^{-1}=1/3\\3^{-2}=(1/3)/3=1/3^2=1/9\\ 3^{-3}=(1/9)/3=1/3^3=1/27[/tex]

And this pattern continues, with the essential takeaway being that [tex]3^{-x}=1/3^x[/tex]

Try applying that pattern to the equation you've been given, [tex]y=4\cdot2^{-6}[/tex], and see what you get!

Please help me solve 9x+16=4x-19

Answers

First you do the order of operations, so it'd be 9x-4x=-19-16. As you can see I've changed some of the powers when you move numbers in an equation the sign (+,-) get flipped. Hope this helps

This is how to solve the equation :)

find decimal notation 75 percent

Answers

The answer is .75 or 1/7 + 5/100 = .75

Hope this helps!

The area of a circle is 25 in. What is it’s radius?

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~ \begin{cases} r=radius\\ -----\\ A=25 \end{cases}\implies 25=\pi r^2\implies \cfrac{25}{\pi }=r^2 \implies \sqrt{\cfrac{25}{\pi }}=r[/tex]

Write 12.5% as a fraction or mixed number in simplest form

Answers

12.5% in decimal form is 0.125

1/8 = 0.125

Your answer = 1/8

Answer: 1/8

Step-by-step explanation: A percent is a ratio that compares a number to 100. So we can write 12.5% as 12.5/100.

Next, we need to get rid of the decimal. We can multiply the numerator and denominator of a fraction by the same number without changing the value of the fraction.

So to get rid of the decimal, we can multiply the numerator and the denominator of 12.5/100 by 10 and we have 125/1000.

Now, notice that 125/1000 is not in lowest terms because we can divide the numerator and the denominator by 125 to get 1/8.

So 12.5% can be written as the fraction 1/8.

A package of 10 cans of soup costs $14. An individual can costs $2. You need at least 25 cans. Find the price of each combination of items.You decide to buy 3 packages of 10 cans. How much do you pay for each can?

Answers

$14×3=$42 price per package of 10
25×$2=$50 individual can cost
30×$2=$60, cost of cans individually bought
so the third problem would be the correct answer because it asks how much for each can

Answer:

$1.4

Step-by-step explanation:

Given, Price of a package of 10 cans = $14

and, Price of an individual can = $2

Now, if I have to purchase at least 25 cans their are two possible ways:

Purchasing 2 packages of the can and then purchase rest individual cans. Thus, if I have to purchase 25 cans it costs: 14 × 2 + 5 × 2 = $38.Purchasing 3 packages of cans. It will cost me: 3 × 14 = $42. But it will give me an extra 5 cans.

Further, if I decided to buy 3 packages of 10 cans it will cost me $42 and I will pay $1.4 for each can.

which is greater - 0.2 ml. or 0.15 ml.

Answers

0.15 ml is greater than -0.2 ml by 0.17 ml

hope this helps

.15 because it is positive

What is the value of this expression? (−8)3

Answers

-24 hope this hellllpsssssss ^_^

=-24

Use the Rules for Signs for Multiplication

then multiply the numbers

A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet. To the nearest whole unit, what is the area of the canvas, including the floor? Use 3.14 for π.

Answers

Answer:

The area of the canvas, including the floor is 1548 sq. feet.

Step-by-step explanation:

Given : A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet.

To find : What is the area of the canvas, including the floor?

Solution :

A conical tent made of canvas has a base that is 34 feet.

The diameter of the base is D=34 feet.

The radius of the base is [tex]r=\frac{34}{2}=17[/tex]

The slant height l=12

The area of the canvas, including the floor is

[tex]A=\pi r l+\pi r^2[/tex]

[tex]A=\pi r(l+r)[/tex]

[tex]A=3.14\times 17(17+12)[/tex]

[tex]A=3.14\times 17\times29[/tex]

[tex]A=1548.02[/tex]

In nearest whole unit, A=1548 sq. feet.

Therefore, The area of the canvas, including the floor is 1548 sq. feet.

Which of the following are good ideas to use when gathering your resources? Check all that apply

A. List potential formulas.
B. Draw a diagram.
C. Guess at the solution and see if you are close.
D. Write down the facts.
E. Form an equation.
F. Organize into a table.

Answers

B. Draw a diagram.

E. Form an equation.

F. Organize into a table.

A. List potential formulas.

And

D.

When gathering resources for problem-solving, the following ideas can be helpful:

A. List potential formulas.B. Draw a diagram.D. Write down the facts.E. Form an equation.F. Organize into a table.

The given options are all effective strategies that can assist in organizing and understanding the problem, as well as formulating a solution.

Option C, guessing at the solution, might not always be reliable or effective in all scenarios and is not considered a systematic approach.

Therefore, it may not be considered a recommended idea when gathering resources for problem-solving.

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How many diameters can a circle have?

Answers

1. But you are actually counting how many lines across a circle can have, then it is infinite.

a circle will never have an exact number of diameters because it is a perfect round circle. you can draw a perfect circle and draw lines across from each angle you will never stop. that is why it will never have an exact number of diameters because it is infinite.

A submarine is 671 feet below sea level. If it ascends 218 feet and then descends 1363 feet, what is its new position?

Answers

Answer:

c = 1816 feet below sea level

Step-by-step explanation:

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