Question 1

Which of the following statements best describes a one-to-one function?

Accepted Answer

Each $$y in $$the range is paired with only one $$x in $$the domain.

Question 2

Which test can be used to determine if a function is one-to-one?

Accepted Answer

Horizontal Line Test

Question 3

Given the function $$f(x) = 2x + 5$$, what is the equation of its inverse?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 4

If $$f(x) = x^3$ + 2$$, which of the following is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x - 2}$$

Question 5

Suppose $$f(x) = \sqrt{x - 2}$$ for $$x \geq 2. $$What is the domain of the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$x \geq 0$$

Question 6

Given $$f(x) = \frac{2x + 3}{x - 4}$$, which of the following is the correct inverse function $$f^{-1}(x$$)$$?

Accepted Answer

Question 7

Which of the following pairs of functions are inverses of each other?

Accepted Answer

$$f(x) = e^x$$ and $$g(x) = \ln(x)$$

Question 8

A function $$f$$ passes the Horizontal Line Test. What does this imply about $$f$$?

Accepted Answer

$$f is a $$one-to-one function.

Question 9

Given the function $$f(x) = 2x - 9$$ used to encode a message, what is the inverse function used to decode the message?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 9}{2}$$

Question 10

If $$f(x)$$ and $$g(x)$$ are inverse functions, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

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

Question 11

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$ (for all real x$)

Question 12

Given the graph of $$f(x)$$, which of the following describes the graph of its inverse $$f^{-1}(x$$)$$?

Accepted Answer

It is a reflection of $$f(x)$$ over the line $$y = x.$$

Question 13

If $$f(x) = x^2$ for x$$ \geq 0$$, what is the inverse function f$$^{-1}$$(x)$$?

Accepted Answer

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

Question 14

Which step is NOT part of the process for finding the equation of an inverse function?

Accepted Answer

Differentiate the function

Question 15

If $$f(x) = 3x - 7$$, and you encode a message using this function, what is the formula to decode the message?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 16

Which of the following is a necessary condition for a function to have an inverse?

Accepted Answer

The function must be one-to-one.

Question 17

Given $$f(x) = x^5$ + 1$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[5]{x - 1}$$

Question 18

If $$f(x) = \sqrt{x - 2}$$ for $$x \geq 2$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 19

A hospital uses the function $$f(x) = 2x - 9 to $$encode patient IDs. If a patient’s encoded ID is 31, what was the original ID?

Accepted Answer

15

Inverse Functions: One-to-One Functions and Their Applications

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