Skip to main content
Student Acer
Race to 1,000:first to win· Win $50 →
← All practice sets

AP Precalculus

AP Precalc 2.7–2.9: Set A Conceptual

Shared by Ashton · Nov 12, 2026 · 0 plays

Composition of functions, inverse functions and logarithmic expressions: the ideas behind them. 16 questions with an explanation for every choice. Concept Check 2.7–2.9 prep.

Report this set

16 questions across 3 sections. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Sections (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

What does $(f \circ g)(x)$ mean?
  1. A. $f(g(x))$: apply g to x first, then apply f to that output. ✓
  2. B. $f(x) + g(x)$: add the two outputs together at the same x.
  3. C. $f(x) \cdot g(x)$: multiply the outputs of f and g at x.
  4. D. $g(f(x))$: apply f to x first, then apply g to that output.

Correct answer: A. The function closest to x acts first, so g goes first and its output is f's input.

Let $f(x) = x + 2$ and $g(x) = 3x$. Which statement is true?
  1. A. $f(g(x)) = g(f(x)) = 3x + 2$ for all x
  2. B. $f(g(x)) = g(f(x)) = 3x + 6$ for all x
  3. C. $f(g(x)) = 3x + 6$ and $g(f(x)) = 3x + 2$
  4. D. $f(g(x)) = 3x + 2$ and $g(f(x)) = 3x + 6$ ✓

Correct answer: D. F(g(x)) = 3x + 2. g(f(x)) = 3(x + 2) = 3x + 6. Different, so order matters.

Which describes the domain of $(f \circ g)(x)$?
  1. A. All x in the domain of g for which g(x) is in the domain of f ✓
  2. B. All x in the domain of f for which f(x) is in the domain of g
  3. C. Every x that is in the domain of f or in the domain of g
  4. D. Exactly the domain of the simplified expression for f(g(x))

Correct answer: A. X must go into g, and then g's output must be allowed into f.

Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. What is the domain of $f(g(x))$?
  1. A. $x \le 0$
  2. B. $x \ge 0$ ✓
  3. C. All real numbers
  4. D. $x > 0$

Correct answer: B. F(g(x)) = (√x)² = x, but g must be defined first, and √x needs x ≥ 0.

Selected values of a relation are shown. Is the inverse relation a function?
  1. A. Yes. The original relation is a function, so its inverse is too.
  2. B. Yes. Every x-value in the original table is different from the rest.
  3. C. No. In the inverse, the input 5 is paired with both 1 and 4. ✓
  4. D. No. The original relation has an output of 0, which can't be switched.

Correct answer: C. The original repeats the output 5, so after switching, x = 5 has two y-values.