Question

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

Answer 1

It will always be an even function.

Explanation:

Suppose `f(x)` and `g(x)` are both even.

Then by definition `f(-x) = f(x)` and `g(-x) = g(x)` for all `x` in the domain.

So if `h(x) = f(x)+g(x)` and `j(x) = f(x)-g(x)` then

`h(-x) = f(-x)+g(-x) = f(x)+g(x) = h(x)`

`j(-x) = f(-x)-g(-x) = f(x)-g(x) = j(x)`

So both `h(x)` and `j(x)` satisfy the condition for being even functions.