The composition of a function and its inverse is always

Question

asked Dec 6, 2021 109k views

2 Answers

Jorgeh · Answer 1 · 2021-12-07T22:28:49+0000

Lets try this with an example.

Suppose we have a function
f(x)=2x .

Calculate its inverse
f^(-1)(x)=(x)/(2) .

And now just simply try to find the composition,

$f(f^(-1)(x))=f\Big((x)/(2)\Big)=2\cdot(x)/(2)=x$ .

The answer is the composition of a function and its inverse is always function
$g(x)=f(f^(-1)(x))=\boxed{x}$ .

Hope this helps.