If g is the inverse of a function f and [f'( x ) = 1 1 + x^5,] then [g'( x )] is equal to:

Question

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 $x=g(y)$

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

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

Solutions · 1