AP® Precalculus: Composition of Functions — Drill 1

About This Drill

AP® Precalculus: Composition of Functions — Drill 1 is a Math practice drill covering composition-of-functions. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice evaluating and analyzing composed functions on the AP® Precalculus exam. These five questions cover table-based evaluation, symbolic simplification, domain restrictions, and interpreting compositions in real-world contexts — skills tested across all three sections of the AP® exam.

Questions in This Drill

1. The tables below give selected values of f and g.
   
   

   x	1	2	3	4
   f(x)	3	1	4	2

   x	1	2	3	4
   g(x)	4	3	2	1

   
   What is the value of f(g(2))?
2. Let f(x) = 2x − 1 and g(x) = x² + 3. Which of the following is an expression for (f ∘ g)(x)?
3. Let f(x) = √x − 4 and g(x) = x². What is the domain of (f ∘ g)(x)?
4. A company's monthly profit P (in thousands of dollars) depends on the number of units sold n according to P(n) = 0.4n − 8. The number of units sold depends on the price per unit p (in dollars) according to n(p) = 200 − 5p. Which of the following expresses the monthly profit as a function of price?
5. Functions f and g are defined by f(x) = \(\dfrac{1}{x-2}\) and g(x) = \(\dfrac{3}{x}\). For what value(s) of x is (f ∘ g)(x) undefined?