Question

If f(x) is a function which is odd and even simultaneously, then f(3) - f(2) is equal to

Answer 1

The only functions which are both odd and even simultaneously are of the form:

f(x) = 0.

So, f(3) - f(2) = 0 - 0 = 0.

Answer 2

Value of f(3) - f(2) is 0.

Given:

f(x) is a function which is odd and even simultaneously.

To Find:

Value of f(3) - f(2).

Solution:

According to the question,

f(-x) = f(x) (Since, it is an even function) -- eq1

f(-x) = -f(x) (Since, it is an odd function) --eq2

Equating equation 1 and 2 we get:

⇒f(x) = -f(x)

⇒2f(x) = 0

which implies that for all values of x f(x) = 0.

Therefore, f(3) = 0 & f(2) = 0.

Thus, f(3) - f(2) = 0.

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