Let $f : ( 0 , \infty ) \rightarrow \mathbb { R }$ be a continuous function such that for all $x \in ( 0 , \infty )$, $$f ( 2 x ) = f ( x )$$ Show that the function $g$ defined by the equation $$g ( x ) = \int _ { x } ^ { 2 x } f ( t ) \frac { d t } { t } \text { for } x > 0$$ is a constant function.