Let be a differentiable function with inverse such that

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

Problem

Let ff be a differentiable function with inverse gg such that f(a)=bf(a)=b. State the necessary condition on f′(a)f'(a) for g′(b)g'(b) to exist.

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