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 ?
Periodicity of a function.
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functional-equations
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1Since you are new, I want to give you some advice about the site: **To get the best possible answers, you should explain what your thoughts on the problem are so far**. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people are much more willing to help you if you show that you've tried the problem yourself. – 2012-12-21
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0*Hint:* How does multiplying your input $x$ by a constant $k$ change the periodocity? – 2012-12-21
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0@ZevChonoles See, I know that probably the product of two functions probably has a period equal to the L.C.M. of their individual periods. Same for the sum. The only problem was verifying the procedure and the answer. – 2012-12-22