1) if g(x) is the inverse function of f(x) and $f'(x) =\frac{1}{1+x^{4}}$ , then g'(x) is A) $1+[g(x)]^{4}$ B) $1-[g(x)]^{4}$ C) $1+[f(x)]^{4}$ D) $\frac{1}{1+[g(x)]^{4}}$ Answer: Option AExplanation:Given, g(x)=f'(x) f(g(x))=x On differentiating both sides w.r.t 'x' , we get f'(g(x)).g'(x)=1 $\therefore$ $\frac{1}{1+(g(x))^{4}}g'(x)=1$ $[\because f'(x)=\frac{1}{1+x^{4}}(given)]$ $\Rightarrow g'(x) =1+[g(x)]^{4}$
