This function is odd or even?

Question

If x, -x ∈ the function of F. then 1/2 [f(x) - f(-x)] is always:

1) Even
2) Odd

3) Neither even nor odd

4) one-to-one

Answer 1

Do you understand what the first part (up to the period) of the statement of this submission intended?

Answer 2

Let g(x) = (1/2)[f(x) - f(-x)]

 

g(-x) = (1/2)[f(-x) - f(-(-x))]

 

        = (1/2)[f(-x) - f(x)]

 

        = -(1/2)[f(x) - f(-x)] = -g(x)

 

Since g(-x) = -g(x), g(x) is an odd function.