If f and t are both even functions, is the product ft even? if f and t are both odd functions, is ft odd? what if f is even and t is odd? justify your answers.

(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

The function ft is even function.

(c)

Let f is even and t odd function, then

The product of both functions is

The function ft is odd function.

the answer is c. 23/3