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Question: Let f : R ® R be a one onto differentiable function, such that f(2) = 1 and f'(2) = 3, then the valu...

Let f : R ® R be a one onto differentiable function, such that f(2) = 1 and f'(2) = 3, then the value of (ddx(f−1(x)))x=1\left( \frac{d}{dx}(f^{- 1}(x)) \right)_{x = 1} is –

A

12\frac{1}{2}

B

13\frac{1}{3}

C

16\frac{1}{6}

D

6

Answer

13\frac{1}{3}

Explanation

Solution

Let f–1(x) = g(x)

So g ¢(x) = 1f′(g(x))\frac{1}{f'(g(x))}

g ¢(1) = 1f′(g(1))=1f′(2)=13\frac{1}{f'(g(1))} = \frac{1}{f'(2)} = \frac{1}{3}