Let `g(x)` be the inverse of an invertible function `f(x)` which is derivable at `x=3` . If `f(3)=9` and `f^(prime)(3)=9` , write the value of `g^(prime)(9)` .

Explanation

We have , `f(3)=9, f^{prime}(3)=9`

and `g(x)=f^{-1}(x)`


`Rightarrow(g o f)(x)=x `

`Rightarrow g{f(x)}=x `

`Rightarrow frac{d}{d x}[g{f(x)}]=1 `

`Rightarrow g^{prime}{f(x)} frac{d}{d x}{f(x)}=1 `

`Rightarrow g^{prime}{f(x)} times f^{prime}(x)=1 `

...