Question

Question #0a2db

Answer 1

Assuming that you are studying real valued functions of real numbers, the answer is Yes if `0` is in the domain of `f`.

Explanation:

`f` is odd if and only if `f(-x)=-f(x)` for all `x` in the domain of `f`.

If `0` is in the domain of odd function `f`, then `f(-0) = -f(0)`.
But `-0=0` so `f(0)=-f(0)`.
This implies `f(0)=0`

Note that `f(x) = 1/x` is an odd function with `0` NOT in the domain.