# Is the product of two even functions even or odd? [closed]

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)?

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

Proof: $h(-x)=f(-x)g(-x)=f(x)g(x)=h(x)$.
• This ought to end by saying $\cdots=h(x). \qquad$ – Michael Hardy Sep 2 '18 at 4:45