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

Question

5298 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-17T21:35:36

See below.

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:

enter image source here

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