Question
Download Solution PDFIf the function f is differentiable at x = c and is one-one in some neighbourhood of c, g is inverse function of f, then g'{f(c)} is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If g is the inverse function of f then gof(x) = g(f(x)) = x
Chain rule of differentiation: [g(f(x))]' = g'(f(x)).f '(x)
Calculation:
Given, the function f is differentiable at x = c and is one-one in some neighborhood of c, g is the inverse function of f,
⇒ g(f(x)) = x
Differentiating both sides with respect to x,
⇒ g'(f(x)).f '(x) = 1
⇒ g'(f(x)) = \(\rm \frac{1}{f'(x)}\)
So, at x = c,
g'(f(c)) = \(\rm \frac{1}{f'(c)}\)
∴ The correct option is (1).
Last updated on Jun 18, 2025
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