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Question: Let f & g are differentiable function which satisfies g ′(m) = 4 & g(m) = b and fog(x) is an identit...

Let f & g are differentiable function which satisfies g ′(m) = 4 & g(m) = b and fog(x) is an identity function then f ′(2) is

equal to

A

4

B

43\frac{4}{3}

C

14\frac{1}{4}

D

34\frac{3}{4}

Answer

14\frac{1}{4}

Explanation

Solution

f(g(x)) = x ⇒ f ′(g(x)) g ′(x) = 1

f ′(g(m)) g ′(m) = 1 ⇒ f ′(2) 4 = 1 ⇒ f ′(2) = 14\frac{1}{4}