Question

determine if h(x)=5/x+2 is an inverse of f(x)=5/x-2

Answer 1

The definition of an inverse:
\[
f((h(x))=h(f(x))=x
\]So, does:
\[
\frac{5}{f(x)+2}=\frac{5}{\frac{5}{x-2}+2}=x?
\]