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Q.
If $g(x)$ is the inverse function of $f(x)$ and $f' (x) = \frac{1}{1 + x^4} $ then $g'(x)$ is
MHT CETMHT CET 2017Relations and Functions - Part 2
Solution:
$g=f^{-1} $
$f(g(x))=x$
Differentiate w.r.t.x
$f '( g ( x )) \cdot g '( x )=1$
$\therefore \frac{1}{1+( g ( x ))^{4}} \cdot g'( x )=1 $
$g'( x )=1+[ g ( x )]^{4}$