12. a real-valued function f defined on the real line is called an even func- tion if f(-t) = f(t) for each real number t. prove that the set of even functions

12. A real-valued function f defined on the real line is called an even func- tion if f(-t) = f(t) for each real number t. Prove that the set of even functions defined on the real line with the operations of addition and scalar multiplication defined in Example 3 is a vector space.