AP Calculus ABhardmcq1 pt

A one-to-one differentiable function ff satisfies f(1)=9f(1)=9, f(2)=5f(2)=5, f(3)=4f(3)=4, f(1)=2f'(1)=2, f(2)=6f'(2)=6, and f(3)=10f'(3)=10. What is (f1)(9)(f^{-1})'(9)?

A.22
B.12\dfrac{1}{2}
C.16\dfrac{1}{6}
D.99

Explanation

Core Concept

The value 9 is f(1)f(1), so f1(9)=1f^{-1}(9)=1. The formula gives (f1)(9)=1f(1)=12(f^{-1})'(9)=\frac{1}{f'(1)}=\frac{1}{2}.

Correct Answer

B12\dfrac{1}{2}

More Unit 3: Differentiation: Composite, Implicit, and Inverse Functions practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 3: Differentiation: Composite, Implicit, and Inverse Functions Questions →