If is differentiable and invertible with and

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If ff is differentiable and invertible with f(a)=bf(a)=b and f′(a)≠0f'(a)\neq 0, what is the value of (f−1)′(b)(f^{-1})'(b)? (a) f′(a)f'(a) (b) 1f′(b)\displaystyle \frac{1}{f'(b)} (c) 1f′(a)\displaystyle \frac{1}{f'(a)} (d) −1f′(a)\displaystyle -\frac{1}{f'(a)}

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