Question

Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.

Answer 1

f(x)=f(-x) definition of even function
g(x)=g(-x) definition of even function
f(x)+g(x)=f(-x)+g(-x) Addition property of equality
h(-x)=f(-x)+g(-x) Definition h(x)
h(x)=h(-x) Substitution
h(x) is even by definition of even function
Hope this helps!Good Luck!

Answer 2

yes, it is.

Explanation:

An even function is that where for any x, f(-x)=-f(x).

So, suppose that f(x) and g(x) are even functions and define h(x)= f(x)+g(x). Then:

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

= -f(x)+(-g(x)) because f and g are even functions.

= -f(x)-g(x)

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

= -h(x).

Then, h(x) is an even function.