US Common Core State Standards (CCSS) Class 10 Algebra II MCQs: Inverse Functions

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Inverse Functions

   1.

   Which of the following functions has an inverse that is also a function?

   1. (A)

      $f(x) = 2x+3$

   2. (B)

      $f(x) = \sin(x)$

   3. (C)

      $f(x) = x^2$

   4. (D)

      $f(x) = |x|$

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   Answer: (A)

   $f(x) = 2x+3$

   Inverse Functions · Easy

2. 2.

   What is the inverse of the function $f(x) = 3x - 5$?

   1. (A)

      $f^{-1}(x) = 3x+5$

   2. (B)

      $f^{-1}(x) = 5x - 3$

   3. (C)

      $f^{-1}(x) = \frac{x-5}{3}$

   4. (D)

      $f^{-1}(x) = \frac{x+5}{3}$

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   Answer: (D)

   $f^{-1}(x) = \frac{x+5}{3}$

   Inverse Functions · Medium

3. 3.

   Given $g(x) = \sqrt{x-2}$ for $x \ge 2$, what is the domain of its inverse function $g^{-1}(x)$?

   1. (A)

      $x \ge -2$

   2. (B)

      All real numbers

   3. (C)

      $x \ge 2$

   4. (D)

      $x \ge 0$

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   Answer: (D)

   $x \ge 0$

   Inverse Functions · Hard

4. 4.

   If $h(x) = \frac{1}{x+4}$, what is $h^{-1}(x)$?

   1. (A)

      $h^{-1}(x) = \frac{1}{x} + 4$

   2. (B)

      $h^{-1}(x) = x-4$

   3. (C)

      $h^{-1}(x) = \frac{1}{x} - 4$

   4. (D)

      $h^{-1}(x) = x+4$

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   Answer: (C)

   $h^{-1}(x) = \frac{1}{x} - 4$

   Inverse Functions · Medium

5. 5.

   For a function $f(x)$ and its inverse $f^{-1}(x)$, which statement is always true?

   1. (A)

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

   2. (B)

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

   3. (C)

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

   4. (D)

      The domain of $f(x)$ is the range of $f^{-1}(x)$

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   Answer: (C)

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

   Inverse Functions · Easy

— End of the paper · updated 1 November 2026 —