Question

How do you find the inverse of `f(x) =1/x`?

Answer 1

`f^(-1)(x)=1/x`

Explanation:

`f(x) = 1/x=>` write `x` as a function of `y:`

`y = 1/x=>` switch `x and y:`

`x = 1/y=>` solve for `y:`

`y=1/x=>` this is the inverse function of `f(x):` hence

`f^(-1)(x)=1/x`

To check let`:f(x)=1/x , g(x)=1/x:`

`g(f(x)) = 1/(1/x) = x` and`f(g(x))=1/(1/x)=x:`

hence `g` is the inverse of `f` and `f` is the inverse of `g.`