AP Precalculus
AP Precalc 2.7–2.9: Set B Solving
Shared by Ashton · Nov 12, 2026 · 0 plays
Evaluate compositions, find domains, decompose functions, find inverses (including rational functions), read inverse values from tables and graphs, and evaluate logarithms. 20 questions with an explanation for every choice. Concept Check 2.7–2.9 prep.
20 questions across 3 sections. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
Let $f(x) = 3x - 5$ and $g(x) = 2x + 1$. Find $f(g(-2))$.
- A. −11
- B. −14 ✓
- C. −21
- D. 33
Correct answer: B. G(−2) = −3, then f(−3) = −9 − 5 = −14.
Let $f(x) = 4x - 5$ and $g(x) = x^2 - 2x + 4$. Find $f(g(x))$.
- A. $4x^2 - 8x + 11$ ✓
- B. $16x^2 - 48x + 39$
- C. $x^2 + 2x - 1$
- D. $4x^2 - 8x - 1$
Correct answer: A. 4(x² − 2x + 4) − 5 = 4x² − 8x + 16 − 5.
Let $h(x) = 3(2)^x$ and $k(x) = 3 - 2x$. Which is equivalent to $h(k(x))$?
- A. $24\left(\frac{1}{4}\right)^x$ ✓
- B. $\frac{3}{8}\left(\frac{1}{4}\right)^x$
- C. $3 - 6(2)^x$
- D. $24(4)^x$
Correct answer: A. 3·2^(3 − 2x) = 3·2³·(2⁻²)^x = 24(1/4)^x.
Let $f(x) = x^2 - 3x$ and $g(x) = \frac{1}{x+2}$. What is the domain of $(g \circ f)(x)$?
- A. All real numbers except 1 and 2 ✓
- B. All real numbers
- C. All real numbers except x = −2
- D. All real numbers except x = 0 and x = 3
Correct answer: A. G(f(x)) = 1/(x² − 3x + 2) = 1/((x − 1)(x − 2)), so x ≠ 1, 2.
Let $g(x) = \frac{1}{x+2}$ and $h(x) = \sqrt{x}$. What is the domain of $(h \circ g)(x)$?
- A. All real numbers except −2
- B. $(-\infty, -2)$
- C. $(-2, \infty)$ ✓
- D. $[-2, \infty)$
Correct answer: C. H(g(x)) = 1/√(x + 2) needs x + 2 > 0: positive under the root and nonzero in the denominator.