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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
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B
2
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C
23
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D
None of these
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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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