Answer
Yes, f has an inverse.
$f^{-1}(1)=4$,
$f^{-1}(3)=5.$
Work Step by Step
The graph passes the Horizontal Line Test
(any horizontal line that intersects the graph, does so in only one point).
The function is one-to-one and has an inverse.
If (a,b) is on the graph, this means that $f(a)=b$ and $f^{-1}(b)=a.$
The point $(4,1)$ is on the graph, so $f^{-1}(1)=4.$
The point $(5,3)$ is on the graph, so $f^{-1}(3)=5.$