Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x)=2/x and g(x)=2/x

Answer 1

It's a little confusing because x is used in different ways.. Start with
g(x) = 2/x
Now substitute that into
f(g(x)) = 2/g(x) = 2/ (2/x) = x

And since f(x) = g(x) we're done by symmetry. Just switch letters.

Answer 2

@telliott99 thank you