+339 Fill in the blanks.
If f(x) is an even function and g(x) is an even function and h(x) is an even function, then f(x) + g(x) + h(x) is an ___ function.
If f(x) is an odd function and g(x) is an odd function and h(x) is an even function, then f(x)*g(x) + h(x) is an ___ function.
If f(x) is an even function and g(x) is an odd function and h(x) is an odd function, then f(x)*(g(x) + h(x)) is an ___ function.
If f(x) is an odd function and g(x) is an even function and h(x) is an odd function, then f(x)*g(x)*h(x) is an ___ function.
+113 Even Function Properties: An even function satisfies the condition f(x) = f(-x).
Odd Function Properties: An odd function satisfies the condition f(x) = -f(-x).
Sum of Even Functions: The sum of even functions is always an even function.
Product of Even and Odd Functions:
Even * Even = Even
Even * Odd = Odd
Odd * Odd = Even
Sum of Even and Odd Functions: The sum of an even and an odd function is neither even nor odd, unless the terms cancel out.
