A) \[\frac{1}{1+{{(g(x))}^{3}}}\]
B) \[\frac{1}{1+{{(f(x))}^{3}}}\]
C) \[1+{{(g(x))}^{3}}\]
D) \[1+{{(f(x))}^{3}}\]
Correct Answer: C
Solution :
Since \[g(x)\]is the inverse of \[f(x)\], therefore \[f(x)=y\]\[\Leftrightarrow g(y)=x\] Now, \[g'(f(x))=\frac{1}{f'(x)}\,,\,\forall x\]Þ \[g'(f(x))=1+{{x}^{3}},\ \ \forall x\] Þ \[g'(y)=1+{{(g(y))}^{3}}\] [using\[f(x)=y\Leftrightarrow x=g(y)]\] Þ \[g'(x)=1+{{(g(x))}^{3}}\] (replacing y by x).You need to login to perform this action.
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