# Periodicity of a function.

If we have two functions $f:\mathbb{R} \to \mathbb{R}$ and $g :\mathbb{R} \to \mathbb{R}$ such that the period of $f$ is 7 and that of $g$ is 11, then the period of $F\left ( x \right ) = f( x)g(\frac{x}{5}) + g(x)f(\frac{x}{3})$ is ?

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Hint: How does multiplying your input $x$ by a constant $k$ change the periodocity? –  Rustyn Dec 21 '12 at 8:21