Answer
(a) $(-5,3)$
(b) $(-5,-3)$
Work Step by Step
(a) We know that for an even function, $f(-x)=f(x)$.
If point $(5,3)$ is on the graph of an even function $f$, then
$f(5)=3$
$\implies$ $f(-5)=f(5)=3$.
The point $(-5,3)$ must also be on the graph.
(b) We know that for an odd function, $f(-x)=-f(x)$.
If point $(5,3)$ is on the graph of an odd function $f$, then
$f(5)=3$
$\implies$ $f(-5)=-f(5)=-3$.
The point $(-5,-3)$ must also be on the graph.
