Question

If f(x) and g(x) are respectively an even and odd functions, then the function f(x). g(x) is:
(a) an even function.
(b) an odd function.
(c) either even or odd function.
(d) neither even nor odd function.​

Answer 1

Answer:

A function with a graph that is symmetric about the origin is called an odd function. Note: A function can be neither even nor odd if it does not exhibit either symmetry. ... Also, the only function that is both even and odd is the constant function f(x)=0 f ( x ) = 0 .

Answer 2

Answer:

The answer is Option (c) either even or odd function.

Explanation:

Assume that the function f is a real-valued function of a real variable. When the equation holds true for all values of x such that both x and -x are present in the domain of the function f, the function is odd.

-f(x) = f (-x)

or an equivalent

f(x) + f(-x) = 0

For instance, f(x) = x³ is an odd function since -f(x) Equals f for all values of x. (-x).

Think about the function f(x), where x represents a real number. When we replace x with -x and get the same expression as the original function, the function f(x) is said to be an even function. In other words, if f(-x) = x for all real values of x, the function f(x) is said to be an even function.

Function that is even: f(-x) = f (x)

f(-x) =f(x) (even function)

g(-x) = -g(x) (odd function)

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

Therefore, the answer is (c) either even or odd function.

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