QJEEM14Ma5ee4: JEE Main 2014 Mathematics - Class 12 JEEM14Ma5ee4 Solution: If is the inverse of a function and then is equal to:

Question

Verified Solution • 2025–26 Session moderate

If

g

is the inverse of a function

f

and

f'\left( x \right) = {1 \over {1 + {x^5}}},

then

g'\left( x \right)

is equal to:

Accepted Answer

Since

f(x)

and

g(x)

are inverse of each other

\therefore

g'\left( {f\left( x \right)} \right) = {1 \over {f'\left( x \right)}}

\Rightarrow g'\left( {f\left( x \right)} \right) = 1 + {x^5}

\left( \, \right.

As

\,f'\left( x \right) = {1 \over {1 + {x^5}}}

\left. \, \right)

Here

x=g(y)

\therefore

g'\left( y \right) = 1 + \left\{ {g\left( y \right)} \right\}

\Rightarrow g'\left( x \right) = 1 + \left\{ {g\left( x \right)} \right\}

Step-by-Step Verified Solution