Question

The product of an odd function and an even function is ___function​

Answer 1

Answer:

The product of an even function and an odd function is an odd function. The quotient of two even functions is an even function.

Step-by-step explanation:

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Answer 2

Answer:

The product of an odd function and an even function is an odd function​.

Step-by-step explanation:

To Find:

The product of an odd function and an even function is an odd function​.

Solution:

• Let f(x) be odd and g(x) be even.
• Then, f(-x) = - f(x)  and g(-x)= g(x) for all x.
• Let, h(x) = f(x)g(x)
• Then we can say that:

                           h(-x) = f (-x) g(-x)

                                   = (-f(x)) g(x)

                                   = - (f(x))g(x)

                                   = -(f(x)g(x))

                                   = -h(x)

                                  for all x.

• That is h(x) is odd.
• Thus, we conclude that:

The product of an odd function and an even function is an odd function​.