This set of points is on the graph of a function.
{(−3, 9), (−1, 1), (0, 0), (2, 4)}
Which points are on the graph of the inverse?
Select each correct answer.
(0, 0)
(−9, 3)
(4, 2)
(1, −1)
What is the inverse of f(x)=4x+3 ?
f^−1(x)=1/4x−3/4
f^−1(x)=−1/4x+3/4
f^−1(x)=4x−3
f^−1(x)=−4x−3
What is the inverse of the function?
g(x)=−4/3x+2
g^−1(x)=−4/3x−2
g^−1(x)=3/4x+2/3
g^−1(x)=−3/4x+3/2
g^−1(x)=4/3x−2
Which functions are invertible?
Select each correct answer. (has pictures)
A.
B.
C.
D.
What is the inverse of f(x)=x4+7 for x≥0 where function g is the inverse of function f?
g(x)=x+7√4 , x≥−7
g(x)=x√4+7 , x≥0
g(x)=x−7√4, x≥7
g(x)=x√4−7 , x≥0
Answers
(-3,9) is one point on the original function, so (9,-3) is on the inverse. We swap x and y. The point (9,-3) isn't listed so we move onto the next.
(-1,1) is on the original so (1,-1) is on the inverse. Again we swap x and y. Choice D matches with this. So D is one of the answers.
Choice A is also an answer since (0,0) swaps to (0,0)
Choice C is also an answer since (2,4) swaps to (4,2)
In summary, the answers are A, C, D
======================================================================
Problem 2)
Replace f(x) with y. Swap x and y. Then solve for y
f(x) = 4x+3
y = 4x+3
x = 4y+3
x-3 = 4y+3-3
x-3 = 4y
4y = x-3
4y/4 = (x-3)/4
y = (x-3)/4
y = x/4-3/4
y = (1/4)x-3/4
which matches with choice A, so choice A is the answer
======================================================================
Problem 3)
Replace g(x) with y. Swap x and y. Then solve for y
g(x) = (-4/3)x + 2
y = (-4/3)x + 2
x = (-4/3)y + 2
x-2 = (-4/3)y + 2-2
x-2 = (-4/3)y
(-3/4)(x-2) = (-3/4)(-4/3)y
(-3/4)(x-2) = y
y = (-3/4)(x-2)
y = (-3/4)x+(-3/4)(-2)
y = (-3/4)x+3/2 ... answer is choice C
======================================================================
Problem 4)
The first two are invertible while the last two are not. The last two fail the horizontal line test so they don't have an inverse.
======================================================================
Problem 5)
It's a bit tricky to determine what the answer choices are saying but I'm assuming they are referring to fourth roots. If so, then we have
f(x) = x^4+7
y = x^4+7
x = y^4+7
x-7 = y^4+7-7
x-7 = y^4
y^4 = x-7
FourthRoot(y^4) = FourthRoot(x-7)
y = FourthRoot(x-7)
which is written as [tex]\sqrt[4]{x-7}[/tex]
The points on the inverse function are (9, -3), (1, -1), (0, 0), and (4, 2). The inverse of f(x)=4x+3 is[tex]f^{-1}(x) = -3 + \frac{1}{4}x[/tex]. The inverse of g(x)=−4/3x+2 is [tex]g^{-1}(x) = \frac{3}{4}x + \frac{2}{3}[/tex] . The inverse of f(x)=x^4+7 for x≥0 is [tex]g(x) = \sqrt{\frac{x-7}{4}}[/tex], for x≥7.
Explanation:To find the points on the graph of the inverse of the function, simply switch the x and y coordinates. So, the points on the graph of the inverse function would be (9, -3), (1, -1), (0, 0), and (4, 2).
For the inverse of the function f(x)=4x+3, you rearrange the equation to solve for x. That gives [tex]f^{-1}(x) = -3 + \frac{1}{4}x[/tex]Therefore, the correct answer is [tex]f^{-1}(x) = \frac{1}{4}x - \frac{3}{4}[/tex]
The inverse of the function g(x)=−4/3x+2 could be found in the same way, which gives[tex]g^{-1}(x) = \frac{3}{4}x + \frac{2}{3}[/tex]
As for the question regarding invertible functions, without the images it is not possible to provide an answer.
The inverse of the function [tex]f(x)=x^4+7[/tex] for x≥0 is calculated by swapping x and y, and then solving for y. This yields: [tex]g(x) = \sqrt{\frac{x-7}{4}}[/tex], for x≥7.
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Related Questions
what are properties of an exponent
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Hope this helps!
Simmon made 2/3 of a pound of weighed pizza. He distributed the pizza to 6 of his friends. What was the weight of the pizza that each friend gets?
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Problem page ali made a shirt using 15 meters of yellow fabric and 12 meters of green fabric. how many meters of fabric did he use in all?
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Three students out of a group of 10 seniors will be chosen to speak in front of the school. What is the probability that Ben, Mark, and Ty will be chosen
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hm, if order does not matter
then it is 3/10 that one of the 3 is chosen
assuming that one was chosen, we now have a probablity of 2/9
then the last is 1/8
so the ending probablity will be 3/10 times 2/9 times 1/8 or 6/720 or 1/120
the probablity will be 1/120
if the order does matter then it is
1/10 times 1/9 times 1/8 or 1/720 because there is 1 choice for each
What is the degree of the polynomial 5pq2−3p6+5p6q3−6p3q5 ?
Answers
the degree of this is 9...
because :
5pq^2...this term has a degree of 3
3p^6...this has a degree of 6
5p^6q^3...this has a degree of 9
6p^3q^5....this has a degree of 8
so the degree of the polynomial is the highest one....and that is 9
The degree of the given polynomial [tex]5pq^2-3p^6+5p^6q^3-6p^3q^5[/tex] is 9
Explanation :
The given polynomial is [tex]5pq^2-3p^6+5p^6q^3-6p^3q^5[/tex]
Degree of the polynomial is the highest exponent value of the terms . To find out highest exponent , we add the exponents of each term
[tex]5pq^2----> 1+2=3\\-3p^6--->6\\+5p^6q^3--->6+3=9\\-6p^3q^5---> 3+5=8[/tex]
From this we can see that the highest exponent is 9.
so the degree of the given polynomial is 9
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HELP PLEASE ASAP! BRAINLIESTTTTTT
1. Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
2. Write the equation of the line of best fit using the slope-intercept formula y=mx+b. Show all your work, including the points used to determine the slope and how the equation was determined.
3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
4. Test the residuals of two other points to determine how well the line of best fit models the data.
5. Use the line of best fit to help you to describe the data correlation.
6. Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
7. According to your line of best fit, what is the arm span of a 74-inch-tall person?
My plot:
68 inches 65 inches
68 inches 67 inches
64 inches 64 inches
36 inches 37 inches
61 inches 64 inches
69 inches 70 inches
65 inches 66 inches
70 inches 69 inches
62 inches 61 inches
71 inches 70 inches
64 inches 65 inches
70 inches 72 inches
Answers
If you are dealing with a function or model, you the convention is to use the x-axis for the independent variable, this is the input, while the y-axis is for the output or dependent varibale (which is determined by the independent variable).
what is 2340 divided by 53?
Answers
44.1
The (-) is there because the actual number is 44.1509433962
If a ray divides an angle into two complementary angles, then the original angle measures °
Answers
Answer:
The original angle measures [tex]90^{\circ}[/tex].
Step-by-step explanation:
We are asked to find the measure of original angle, when a ray divides an it into two complementary angles.
We know that two complementary angles add up-to 90 degree.
Therefore, the original angle is a right angle or the measure of original angle is [tex]90^{\circ}[/tex].
Write the following statement as a conditional statement. A kite is a figure with four sides. If a figure has four sides, then it is a kites. If a figure is a kite, then it has four sides. If it is a figure, then it is a kite. If it is a figure, then it has four sides.
Answers
A kite is a figure with four sides.
A conditional statement is also called if-then statement. It is a hypothesis followed by a conclusion.
For our case the conditional statement is:
If a figure has four sides, then it is a kites
Answer:
If a figure has four sides, then it is a kites.
Step-by-step explanation:
A cube has a volume of 729 cubic centimeters. What can be concluded about the cube? Check all that apply. Recall the formula mr021-1.jpg. The side length, s, can be found using the equation mr021-2.jpg This is a perfect cube. The side length is 243 centimeters. The side length is 9 centimeters. Taking the cube root of the volume will determine the side length. If you multiply the volume by three, you can determine the side length.
Answers
Answer:
This is a perfect cube
The side length is [tex]9[/tex] centimeters
Taking the cube root of the volume will determine the side length
Step-by-step explanation:
we know that
The volume of a cube is equal to
[tex]V=s^{3}[/tex]
where
s is the length side of the cube
In this problem we have
[tex]V=729\ cm^{3}[/tex]
Solve for s-------> that means isolate the variable s
Find the length side of the cube s
[tex]s=\sqrt[3]{V}[/tex]
substitute the value of V
[tex]s=\sqrt[3]{729}=9\ cm[/tex] --------> a perfect cube
therefore
Statements
This is a perfect cube--------> Is true
The side length is [tex]9[/tex] centimeters -------> Is true
Taking the cube root of the volume will determine the side length ------> Is true
The side length of the cube is 9cm³ showing that the cube is a perfect cube
Volume of the cubeThe formula for calculating the volume of a cube is expressed as:
V = s³
where:
s is the side length of the cube
Given the following
V = 729cm³
Substitute the given parameters into the formula
729 = s³
s³ = 729
s = 9cm
Hence the side length of the cube is 9cm³ showing that the cube is a perfect cube
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10 and two tens, and then double the amount, and 5, 3, and 2. How much now?
Answers
A bakery offers a sale price of $3.40 for 3 muffins. What is the price per dozen? The price per dozen muffins is $
Answers
In a dozen we have 12.. And 3 x 4 is equal to 12
3 muffins= $3.40
12 muffins= $13.60 (x4)
Hope this helps :))
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Which is true about rigid transformations and circles?
a.a reflection of a circle does not conserve the circle's radius.
b.a circle is only carried onto itself after each one degree rotation.
c.a translation of a circle does not conserve the circle's circumference.
d.a circle's shape is preserved regardless of any rigid transformation?
Answers
A rigid transformation is defined to be one in which the pre-image of the object and its new image after the transformation both have the exact same size and shape. So the answer in this question is:
D. a circle's shape is preserved regardless of any rigid transformation
Answer: D. a circle shape is preserved regardless of any rigid transformation.
Step-by-step explanation:
A. 12.2
B. 13.45
C. 16.87
D. 15.12
Answers
10 is opposite leg
Use the sine
sin x = opp/hyp
sin 55 = 10/x
x = 10/sin 55 = 12.208
Answer: x = 12.2
Which statements must be true?
Select each correct answer.
UW=VW
UV=UK
JK=2VW
UW=12KL
UV¯¯¯¯¯∥JL¯¯¯¯¯
Answers
UV is parallel to JL that's correct
JK is 2VW that's correct
UV and UK aren't congruent
UW and UV aren't congruent
The only correct statements in relation to the given triangle are;
JK = 2VW
UV ║ JL
1) UW = VW; This is not correct because we see that UW forms a parallel line to KV but there is nothing to show about it being equal to VW. 2) UV = UK; This is not correct because there is no sign of them being congruent to each other.3) JK = 2VW; We see that UKVW forms a rhombus. This means that parallel sides are equal. Thus; UK = VW.
Since UK is equal to UJ from the triangle, then;
2UK = JK
Since UK = VW, then; 2VW = JK. Thus, the statement is true.
4) UW = 12KL; This is not correct because UW = KV = KL/2 from the diagram.5) UV ║ JL; This statement is correct because from the diagram UV is a side of the parallelogram UVLW with UV parallel to WL since opposite sides of a parallelogram are equal.Read more at; https://brainly.com/question/7447576
Which plane represents the bottom of the rectangular prism above?
A) Plane DGE
B) Plane AHC
C) Plane FGH
D) Plane EDC
Answers
B
The set of all even whole numbers greater than 4 and less than 12 can be written as
Answers
Hope this helps!
True or false A scalene triangle can be equilateral
Answers
Hence, The statement " A scalene triangle can be equilateral " is false .
What is scalene triangle?A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees.
According to the question
A scalene triangle can be equilateral
Now according to the definition of scalene triangle :
A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.
Therefore ,
It cannot be equilateral .
Hence, The statement " A scalene triangle can be equilateral " is false .
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Find y'' by implicit differentiation. 4x3 + 5y3 = 2
Answers
The value of implicit differentiation of y" of the 4x³ + 5y³ = 2 is [tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2} = 0\\[/tex].
To find y'', or the second derivative of y, by implicit differentiation, we'll differentiate both sides of the equation with respect to x, treating y as a function of x.
Step - 1:
Start by differentiating each term with respect to x using the chain rule:
Differentiating 4x³ with respect to x gives 12x².Differentiating 5y³ with respect to x requires the chain rule. We get 15y²(dy/dx).Since we're differentiating with respect to x, we need to multiply dy/dx by y' to indicate the derivative of y with respect to x.
Step - 2:
The right-hand side of the equation, 2, has a derivative of 0 since it is a constant.
Putting it all together, we have the equation:
[tex]12x^2 + 15y^2 \times \frac{dy}{dx} = 0.[/tex]
Now, to find y'', we differentiate this equation with respect to x, treating dy/dx as a function of x.
Differentiating 12x² with respect to x gives 24x.Differentiating 15y² × dy/dx with respect to x requires the product rule. We get [tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2}[/tex].Step - 3:
The right-hand side of the equation, 0, has a derivative of 0 since it is a constant.
Putting it all together, we have the equation:
[tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2} = 0\\[/tex]
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To find y'' by implicit differentiation from the equation 4x^3 + 5y^3 = 2, differentiate both sides with respect to x, apply the chain and product rules appropriately and then solve for y''.
Explanation:To find the second derivative y'' by implicit differentiation for the equation 4x^3 + 5y^3 = 2, you follow these steps:
Differentiate both sides of the equation with respect to x to find the first derivative (y').Apply the chain rule to differentiate y terms, remembering to multiply by y' (dy/dx) because you are differentiating with respect to x.The differentiation of 4x^3 yields 12x^2, and the differentiation of 5y^3 using the chain rule gives you 15y^2*y'.You then set the derivative equal to 0, because the differential of 2 with respect to x is 0.To find the second derivative (y''), differentiate your expression for y' with respect to x again, applying the chain rule and product rule as necessary.This process will provide you with the value of y''.
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There are 184 students going on a field trip. there is 1 chaperone for four students. 50 students can fit on one bus how many busses with there be
Answers
184 / 4 = 46 chaperones needed
184 + 46 = 230 total people
230/50 = 4.6
5 busses are needed
What set of reflections would carry triangle ABC onto itself?
'triangle ABC on the coordinate plane with point A at 0, 2, point B at 2, 4, and point C at 3, 0.
x-axis, y=x, y-axis, x-axis
x-axis, y-axis, x-axis
y=x, x-axis, x-axis
y-axis, x-axis, y-axis, x-axis
Answers
Try to test apex B to reassure that it is correct.
A rectangle has a length one less than three times the width. If the perimeter is 46 units , find the width and length
Answers
Let l represent the length of the rectangle.
Let w represent the width of the rectangle.
[tex] \left \{ {{2(l+w)=46} \atop {3w-1=l}} \right. [/tex]
Isolate for the l in Equation #2.
[tex]3w-1=l[/tex]
[tex]l=3w-1[/tex]
Substitute Equation #2 into Equation #1.
[tex]2(l+w)=46[/tex]
[tex]2[(3w-1)+w)]=46[/tex]
Combine Like Terms.
[tex]2(4w-1)=46[/tex]
Distribute the Parenthesis.
How? Multiply the terms inside the Parenthesis by the term outside of the Parenthesis.
[tex]2*4w-2*1=46[/tex]
[tex]8w-2=46[/tex]
Add 2 to both sides.
[tex](8w-2)+2=(46)+2[/tex]
[tex]8w=48[/tex]
Divide both sides by 8.
[tex] \frac{8w}{8}= \frac{48}{8} [/tex]
[tex]w=6[/tex]
The Answer Is:
[tex] \left[\begin{array}{ccc}w=6\end{array}\right] [/tex]
The Width is 6 units and the Length is 17 units.
Hope this helps.
-Benjamin
1. Please express your answer in scientific notation.
(6.0 x 10^5) x (3.0 x 10^4) =
A. 18 x 10^20
B. 18 x 10^9
C. 1.8 x 10^20
D. 1.8 x 10^10
Answers
(6.0×3.0)(10^5×10^4)=18×10^9
B
Mrs. Rodriquez has 24 students in her class. Ten of the student or boys. Jeff Claims that the ratio of boys to girls in the class must be 5:12. What is Jeff’s error and how can he correct it?
A. Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls to get a ratio of 10:14 or 5:7.
B. Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls to get a ratio of 14:10 or 7:5.
C. Jeff did not write the ratio in the correct order. He should Of written as 24:10.
D. Jeff did not write the ratio in the correct order. He should of written it as 12:5
Answers
what is the greatest perfect square that,s a factor of 244 ?
Answers
Greatest perfect square that is a factor of 244 is 4 which is the perfect square of 2 .
Given, number 244 .
Firstly the factors of 244 :
244 = 2 × 2 × 61
244 = 4 × 61
Therefore the greatest perfect square that is the factor of 244 will be 4 .
4 is the perfect square of 2.
2² = 4.
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A class consists of 6 girls and 10 boys. if a committee of 3 is chosen at random from the class, find the probability th
Answers
divide 60 by 3
your answer is 20 :)
Hope that made sence
Joe was making mixed nuts. He used 2 1/4 pounds of peanuts and 3 1/5 pounds of cashews. How many pounds of mixed nuts did Joe make?
Answers
2 1/4= 9/4=45/20
3 1/5=16/5=64/20
2. Add the factions
45+64=109
109/20
3. Divide the numerator by the denominator
109/20=5.45
4. Your answer is 5.45 pounds
Answer:
the answer is B.
Step-by-step explanation:
Trust me
3 times the sum of 14 and a number is 57
what the equation to represent this
Answers
3 (n + 14) = 57
One way to find the total cost of a jacket for $55.80 with a sales tax of 2.7% is 55.80+0.027(55.80) write an equivalent expression to show another way to find the total cost
Answers
Final answer:
To find the total cost of a jacket with sales tax, you can either use the given expression or calculate the sales tax separately and add it to the original price.
Explanation:
To find the total cost of a jacket with a sales tax, you can use the expression 55.80 + 0.027(55.80) as mentioned in the question.
Another way to find the total cost is to calculate the sales tax first and then add it to the original price of the jacket. To do this, you need to multiply the original price of the jacket by the sales tax rate (2.7% or 0.027) and then add the result to the original price: 55.80 + (0.027 * 55.80).
PLEASE HELP!!
Which functions have graphs that are steeper than the graph of f(x)=−3x^2 ?
Select all correct answers.
A.)
k(x)=3x^2
B.)
j(x)=2x^2
C.)
g(x)=−4x^2
D.)
h(x)=−2x^2
E.)
m(x)=4x^2
Answers
Positive/negative doesn't affect steepness in this situation so A would be out because it is essentially the same as the problem.
You would have to use graph transformations. When a number is front of the whole equation like how 3 is in front of x^2, it stretches the graph VERTICALLY making the graph MORE STEEP.
So which graphs has the largest coefficient (disregarding the negative signs)
It says graphs (with an s) so it would be C and E.
hope this helps C: