Answer
yes
Work Step by Step
See Inverse Function, p.409.
Let $f$ be a one-to-one function.
Then $g$ is the inverse function of $f$ if
$(f\circ g)(x)=x$ for every $x$ in the domain of $g$,
and $(g\circ f)(x)=x$ for every $x$ in the domain of $f$.
The condition that $f$ is one-to-one in the definition of inverse function is essential.
----------------------
g(f(1))=g(1)=1
g(f(3))=g(3)=3
g(f(5))=g(5)=5
f(g(1))=g(1)=1
f(g(3))=g(3)=3
f(g(5))=g(5)=5
So,
$(f\circ g)(x)=x$ for every $x$ in the domain of $g$,
and $(g\circ f)(x)=x$ for every $x$ in the domain of $f$,
... f and g are inverses.
