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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
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.