If f and g are both even functions, is f + g even?

We will use the concept of an even function to find whether f + g is an even function or not.

Answer: If f and g are even functions, then f + g is an even function.

Let us see how we will use the concept of even function to find whether f + g is an even function or not.

Explanation:

Let us consider a function h(x) = f(x) + g(x)

A function h(x) is an even function if h(-x) = h(x). 

Since f and g are both even functions, so f(x) = f(-x) and g(x) = g(-x)

Substitute -x for x.

Now, h(-x) = f(-x) + g(-x) = f(x) + g(x) = h(x)

We see that h(x) = h(-x) .

Therefore, h(x) is also an even function.