Let g(x) be the inverse of an invertible function f(x) which is differentiable at x = c , then g'(f(c)) equals: - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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Let g (x) be the inverse of an invertible function f (x) which is differentiable at x = c, then g^{'} (f (c)) equals:

Solution & Step-by-step Explanation

Since g (x) is the inverse of f (x), we have: g (f (x)) = x Differentiating both sides with respect to x using the chain rule: g^{'} (f (x)) \cdot f^{'} (x) = 1 g^{'} (f (x)) = \frac{1}{f ^{'} ( x )} At x = c : g^{'} (f (c)) = \frac{1}{f ^{'} ( c )}

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Let g (x) be the inverse of an invertible function f (x) which is differentiable at x = c, then g^{'} (f (c)) equals:

f^{'} (c)

\frac{1}{f ^{'} ( c )}

f (c)

None of these

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