Periodic function/Composition properties/Exercise

Let

$f\colon \mathbb {R} \longrightarrow \mathbb {R}$

be a periodic function and

$g\colon \mathbb {R} \longrightarrow \mathbb {R}$

any function. a) Prove that the composite function ${}g\circ f$ is also periodic.

b) Prove that the composite function ${}f\circ g$ does not need to be periodic.

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