Let gx be the inverse of the function fx and f1(x)=11+x3. Then g1(x) is equal to - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Since $g (x)$ is the inverse of $f (x)$ , therefore $f (x) = y \Leftrightarrow g (y) = x$

Now, $g^{'} (f (x)) = \frac{1}{f^{'} (x)}, \forall x \Rightarrow g^{'} (f (x)) = 1 + x^{3}, \forall x$ $\Rightarrow g^{'} (y) = 1 + (g (y))^{3}$

[using $f (x) = y \Leftrightarrow x = g (y)$ ] $\Rightarrow g^{'} (x) = 1 + (g (x))^{3}$ (replacing y by x)

Let $g (x)$ be the inverse of the function $f (x)$ and $f^{1} (x) = \frac{1}{1 + x^{3}} .$ Then $g^{1} (x)$ is equal to