Let be a differentiable function with inverse

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let ff be a differentiable function with inverse f−1f^{-1}. If f(a)=bf(a)=b and f′(a)≠0f'(a)\neq 0, which of the following gives (f−1)′(b)(f^{-1})'(b) in terms of f′(a)f'(a)? (a) f′(a)f'(a) (b) 1f′(b)\dfrac{1}{f'(b)} (c) 1f′(a)\dfrac{1}{f'(a)} (d) f′(b)f'(b)

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