Question 1

Which of the following steps is NOT part of the standard process for finding the inverse of a function $$f(x)$$?

Accepted Answer

Take the derivative of $$f(x).$$

Question 2

Given $$f(x) = 2x + 7$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{2}$$

Question 3

If $$f(x) = 4x - 7$$ and $$g(x) = \frac{x + 7}{4}$$, which statement is true?

Accepted Answer

$$f$$ and $$g$$ are inverses of each other.

Question 4

Which test can be used to determine if a function has an inverse function?

Accepted Answer

The Horizontal Line Test

Question 5

Suppose $$f(x)$$ passes the horizontal line test. What does this imply?

Accepted Answer

$$f(x)$$ has an inverse function.

Question 6

Given $$f(x) = 4x - 7$$, find $$f(f^{-1}(x$$))$$.

Accepted Answer

$$x$$

Question 7

Which of the following is the correct sequence to verify that two functions are inverses?

Accepted Answer

Show that $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 8

A function $$f(x) is $$graphed. If its inverse $$f^{-1}(x$$)$$ is also graphed, how are their graphs related?

Accepted Answer

They are reflections of each other across the line $$y = x.$$

Question 9

Given the graph shown (vertical and horizontal lines), which test does this graph most closely represent?

Accepted Answer

The Vertical Line Test

Question 10

If $$f(x) is $$not one-to-one, what can you conclude about its inverse?

Accepted Answer

$$f(x)$$ does not have an inverse function.

Question 11

A real-world scenario: The temperature in Celsius $$C is $$related to Fahrenheit $$F by$$ $$F = \frac{9}{5}C + 32. $$What is the inverse function to convert Fahrenheit to Celsius?

Accepted Answer

$$C = \frac{5}{9}(F - 32)$$

Question 12

If $$f(x) = x^3$, what is f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x}$$

Question 13

Which of the following functions does NOT have an inverse function?

Accepted Answer

$$f(x) = x^2$

Question 14

If $$f(x) = 3x - 2$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 2}{3}$$

Question 15

A hospital uses the function $$f(x) = 98.6 + 1.8x to $$convert a patient's temperature $$x in $$Celsius to Fahrenheit. What is the inverse function to convert Fahrenheit to Celsius?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 98.6}{1.8}$$

Inverse Functions: Concepts, Methods, and Graphs

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