Answer
To use the Inverse Function Property, one must exchange the places of $x$ and $f(x)$ and then solve for $f(x)$
Work Step by Step
Procedure:
$f(x)=\frac{1}{x-2}$ Swap places of $x$ and $f(x)$
$x=\frac{1}{f(x)-2}$ Now to solve for $f(x)$. Multiply both sides by $f(x)-2$
$(f(x)-2)(x)=\frac{1}{f(x)-2}(f(x)-2)$ Divide both sides by $x$
$\frac{(f(x)-2)(x)}{x}=\frac{1}{x}$ And finally add 2 to both sides.
$f(x)=\frac{1}{x}+2$ which is equal to $g(x)$
