Answer:
(a) If f and t are both even functions, product ft is even.
(b) If f and t are both odd functions, product ft is even.
(c) If f is even and t is odd, product ft is odd.
Step-by-step explanation:
Even function: A function g(x) is called an even function if

Odd function: A function g(x) is called an odd function if

(a)
Let f and t are both even functions, then


The product of both functions is




The function ft is even function.
(b)
Let f and t are both odd functions, then


The product of both functions is


![ft(-x)=[-f(x)][-t(x)]](https://tex.z-dn.net/?f=ft%28-x%29%3D%5B-f%28x%29%5D%5B-t%28x%29%5D)

The function ft is even function.
(c)
Let f is even and t odd function, then


The product of both functions is


![ft(-x)=[f(x)][-t(x)]](https://tex.z-dn.net/?f=ft%28-x%29%3D%5Bf%28x%29%5D%5B-t%28x%29%5D)

The function ft is odd function.