Function Inverses

Select each graph that shows a function and its inverse.

A and D

Waterloo Park posted the following schedule listing the number of hours an employee works on a given day. Let B(x), T(x), R(x), and S(x) represent the number of hours worked by Bill, Ted, Rufus, and Socrates, respectively, on a given day x. What is the value of the inverse shown below?

S-1 (0) = Friday

Talib is trying to find the inverse of the function to the right. His work appears beneath it. Is his work correct? Explain your answer.

Sample Response: His work is not correct. You first must switch x and y and then solve for y.

Is the inverse of the function shown below also a function? Explain your answer.

Sample Response: If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function.

Danika concludes that the following functions are inverses of each other because f(g(x)) = x. Do you agree with Danika? Explain your reasoning. f(x) = |x| g(x) = -x

Sample Response: She is not correct. She forgot to do g compose f. To verify that functions are inverses of each other, you must also show that g(f(x)) = x. Because g(f(x)) = -x, the functions are not inverses of each other.

Find the values of a through e that make these two relations inverses of each other.

a = -3.8 b = -2.6 c = 1.7 d = 4.4 e = 1

The range values of an inverse are the _______________ values of the original function.

domain

f(x) = 4x − 12

f−1(x) = 1/4x 3

Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}

g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

Choose a true statement.

g(x) is a function because f(x) is one-to-one.

h(x) = 2x - 4 / 3

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

If the graph of an inverse passes the, ___________ you know that the inverse is a function.

vertical-line test

The composition of a function and its inverse is always ___________ .

x

The graph of an inverse is the reflection of the graph of the function over the line ________.

y = x