Question

For the function f, use compisition of functions to show that f^-1 is a given.

let f(x)=(1+x)/x show that f^-1(x)=1/x-1

Answer 1

Explanation:

If we have f(x) and it's inverse, and we compose them

we will get

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

So here we compose

`( (1)/( (1 + x)/(x) - 1) )`

`( (1)/( (1)/(x) + 1 - 1)`

`(1)/( (1)/(x) )`

`x`

So the composition is x, so they are inverses.