Example of function $f,g$ s.t. $f$ continuous, $g$ measurable and $f\circ g$ not measurable.

Question

In my course it's written that if $f$ measurable and $g$ continuous then $g\circ f$ is measurable. But is there example of functions $f$ and $g$ s.t. $f$ continuous, $g$ measurable and $g\circ f$ not measurable ?