A) \[f'(c)\]
B) \[\frac{1}{f'(c)}\]
C) \[f(c)\]
D) None of these
Correct Answer: B
Solution :
Since \[g(x)\] is the inverse of function \[f(x)\], therefore \[gof(x)=I(x)\] for all x. Now \[gof(x)=I(x),\ \ \forall x\] \[\] \[\Rightarrow gof(x)=x,\ \ \forall x\]\[\Rightarrow \]\[(gof)'(x)=1,\ \ \forall x\] Þ \[g'(f(x))f'(x)=1,\ \ \forall x\] (using chain rule) Þ \[g'(f(x))=\frac{1}{f'(x)},\ \ \forall x\Rightarrow g'(f(c))=\frac{1}{f'(c)}\](putting x=c)You need to login to perform this action.
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