AP Precalculus Logarithmic Functions

Question 1

Let f(x) = 2x + 3 and g(x) = x². What is the value of (f ∘ g)(2)?

Accepted Answer

11

Answer

(f ∘ g)(2) = f(g(2)) = f(4) = 2(4) + 3 = 11. The inner function g is applied first.

Question 2

Let f(x) = 3·2ˣ. Which expression gives the inverse function f⁻¹(x)?

Accepted Answer

log₂(x/3)

Answer

Set y = 3·2ˣ, divide by 3 to get y/3 = 2ˣ, then take log₂ of both sides: x = log₂(y/3). Swapping variables gives f⁻¹(x) = log₂(x/3).

Question 3

What is the solution to log₃(x + 2) = 2?

Accepted Answer

7

Answer

Rewriting in exponential form gives x + 2 = 3² = 9, so x = 7.

Question 4

Which expression is equivalent to log(x³√y / z) for positive x, y, z?

Accepted Answer

3 log x + ½ log y − log z

Answer

The quotient rule turns division into subtraction, the product rule turns multiplication into addition, and the power rule brings down exponents (√y = y^(1/2)).

Question 5

What is the domain of f(x) = ln(5 − 2x)?

Accepted Answer

x < 5/2

Answer

The argument of a logarithm must be strictly positive, so 5 − 2x > 0, which gives x < 5/2.

AP Precalculus Practice Test

AP Precalculus Practice Test

AP Precalculus Logarithmic Functions