Question

If $$f$$ and $$g$$ be differentiable function satisfying $$g'(a) =2, g(a)=b$$ and $$fog=I$$ (identity function), then $$f'(b)$$ is equal to

A
12
B
2
C
23
D
None of these

Solution

The correct option is A $$\dfrac{1}{2}$$Since, $$fog=I$$$$\Rightarrow fog (x)=x$$ for all $$x$$ $$\Rightarrow f'\{g(x) \}\cdot g'(x)=1$$ for all $$x$$$$\Rightarrow f'\{g(a) \}\cdot g'(a)=1$$$$\Rightarrow f'\{g(a) \}=\dfrac{1}{g'(a)}=\dfrac{1}{2}$$$$\Rightarrow f'(b)=\dfrac{1}{2}$$Mathematics

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