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Two even functions, say f(x) and g(x), when multiplied together give a function, say h(x). Now will h(x) be always even or odd? Or it can be either of these(case-specific)?

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  • $\begingroup$ h(x) will be even $\endgroup$ – Hercules Sep 2 '18 at 4:38
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    $\begingroup$ What did you attempt? Show what have you tried, we will help you get on track. This is not homework answering site. $\endgroup$ – Prasanna Venkatesan Sep 2 '18 at 4:39
  • $\begingroup$ @OP Please do not completely change the question, especially after it was answered. Rolled back. $\endgroup$ – dxiv Sep 2 '18 at 4:45
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    $\begingroup$ $$h(-x) = f(-x)g(-x) = \big(-f(x)\big) \big(-g(x)\big) = f(x) g(x) = h(x). $$ $$ \text{So } h(-x) = h(x). $$ $\endgroup$ – Michael Hardy Sep 2 '18 at 4:46
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Product of two even functions is even.

Proof: $h(-x)=f(-x)g(-x)=f(x)g(x)=h(x)$.

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    $\begingroup$ This ought to end by saying $\cdots=h(x). \qquad$ $\endgroup$ – Michael Hardy Sep 2 '18 at 4:45

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