Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be a continuous function such that for all $x \in \mathbb { R }$ and for all $t \geq 0$, $$f ( x ) = f \left( e ^ { t } x \right)$$ Show that $f$ is a constant function.
Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be a continuous function such that for all $x \in \mathbb { R }$ and for all $t \geq 0$,
$$f ( x ) = f \left( e ^ { t } x \right)$$
Show that $f$ is a constant function.