Let f and G Be Differentiable Function Satisfying G’ (a) = 2, G (a) = B And fog = I (identity Function) Then, f’(b) Is Equal To:

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Question

Let f and g be differentiable function satisfying g’ (a) = 2, g (a) = b and fog = I (identity function) Then, f’(b) is equal to:

Solution

Correct option is

1/2

We have, fog = I  

⇒      f {g(x)} = x,                     for all x Ïµ R 

∴       f ’ {g(x)}. g' (x) = 1,         for all x Ïµ R 

⇒      ’ (g(a)) = 1/g’ (a)  

⇒      f ’ (b) = 1/2

Testing

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