Please use parenthesis! f(x) = 1/(x-2) not f(x) = (1/x) - 2 and g(x) = (2x + 1)/x, not g(x) = 2x + (1/x).
Multiply top and bottom by x.
= = =
= (Check!)
Again:
Multiply top and bottom by x - 2.
= =
= (Check!)
So f(g(x)) = x and g(f(x)) = x. Thus f and g are inverses.
-Dan