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 :
Let \[f(x)=y\] \[\Rightarrow \]\[x={{f}^{-1}}(y)\] \[\Rightarrow \]\[g(y)=x\] Now, g \[(f(x))=\frac{1}{f(x)}\forall x\] \[=1+{{x}^{3}}\] \[\Rightarrow \]\[g(y)=1+{{\{g(y)\}}^{3}}\] \[\Rightarrow \]\[g(x)=1+{{\{g(x)\}}^{3}}\]
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