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Let f and g be differentiable functions on R such that fog is the identity function. If for some $a, b \in R,$ $g' (a) = 5$ and g(a)=b then f'(b) is equal to:

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$\frac{1}{5}$

$\frac{2}{5}$

answer is A.

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Detailed Solution

$fog (x) = x f (g (x)) = x diff w . r . t .' x' f^{1} (g (x)) g^{1} (x) = 1 x = a f^{1} (g (a)) g^{1} (a) = 1 f^{1} (b) \cdot 5 = 1 f^{1} (b) = \frac{1}{5}$

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