Question

How do you show that `f(x)=1/x` and `g(x)=1/x` are inverse functions algebraically and graphically?

Answer 1

See below.

Explanation:

If `f(x)` and `g(x)` are inverse functions, then:

`f(g(x))=g(f(x))=x`

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

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

`x=x=x`

Since these are there own inverses we would expect their graphs to be symmetrical about the line `y=x`

The graph below confirms this: