When you add or subtract two even functions, what type of function will you get?

Oct 18, 2015

It will always be an even function.

Explanation:

Suppose $f \left(x\right)$ and $g \left(x\right)$ are both even.

Then by definition $f \left(- x\right) = f \left(x\right)$ and $g \left(- x\right) = g \left(x\right)$ for all $x$ in the domain.

So if $h \left(x\right) = f \left(x\right) + g \left(x\right)$ and $j \left(x\right) = f \left(x\right) - g \left(x\right)$ then

$h \left(- x\right) = f \left(- x\right) + g \left(- x\right) = f \left(x\right) + g \left(x\right) = h \left(x\right)$

$j \left(- x\right) = f \left(- x\right) - g \left(- x\right) = f \left(x\right) - g \left(x\right) = j \left(x\right)$

So both $h \left(x\right)$ and $j \left(x\right)$ satisfy the condition for being even functions.