Answer
No inverse
Work Step by Step
Using the graph, determine the values of $f$ for each of the values of $x\in\{1,3,4,6\}$:
$f(-4)=3$
$f(-2)=4$
$f(0)=0$
$f(3)=-1$
So we have the points:
$(-4,3),(-2,4),(0,0),(3,-1)$
Check if the given function $f$ passes the Horizontal Line Test: we notice that there is a horizontal line which intersects the graph at more than one point; therefore the function fails the test, so it has no inverse.
If $(a,b)$ belongs to the graph of $f$, then $(b,a)$ belongs to the graph of $f^{-1}$. In order to determine the inverse $f^{-1}(x)$ we consider the ordered pairs:
$(1,1),(2,3),(6,4),(7,6)$
Plot the points and join them by segments to graph $f^{-1}$:
