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Let f and g be differentiable functions satisfying  \mathrm{g^{\prime}(a)=2, g(a)=b ~and ~f o g=I} (identify function). Then  \mathrm{f^{\prime}(b)}  is equal to

Option: 1

\frac{1}{2}


Option: 2

2


Option: 3

\frac{2}{3}


Option: 4

none of these


Answers (1)

best_answer

\mathrm{ f o g=I \Rightarrow f \circ g(x)=x \text { for all } x }
\mathrm{ \Rightarrow f^{\prime}(g(x)) g^{\prime}(x)=1 \text { for all } x }

\mathrm{ \Rightarrow f^{\prime}(g(a))=\frac{1}{g^{\prime}(a)}=\frac{1}{2} \\ }

\mathrm{ \Rightarrow f^{\prime}(b)=\frac{1}{2} }
 

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Divya Prakash Singh

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