Question

Find

(f ⁻¹)'(a).

f(x) = 6 + x² + tan(πx/2),    −1 < x < 1,    a = 6

Answer 1

We need to find the value of differentiated inverse function of y = f(x) at x = 6.

let inverse of function f(x) is g(x). That is :

thus

Given :

Put x = 0

we get :

Replacing x with inverse function of f(x) in the given f(x).

differentiating both side with respect to x ,

Put x = 6, (domain of x is not -1<x<1, it is actually range of f(x). Thus we can put x = 6)

Using g(6) = 0

{sec(0)=1}

or answer