Answer
True
Work Step by Step
The y-intercept of a function $k(x)$ is $ Y=k(0)$, the x-intercept is $X$ such that $k(X)=0$
So, $f(0)=X$
$⇒ f^{-1}(f(0)) = f^{-1}(X) $
$ ⇒ f^{-1}(X) =0$ which is, by definition, the x-intercept of the function $f^{-1}(x)$