2006-09-11 18:58:15 · 5 answers · asked by ttybrs10 1 in Science & Mathematics ➔ Mathematics
Hmm, I've never heard of this property before, but let's see. An odd function if a function so that f(-x) = -f(x). Well but 0 has the property that -0=0. That means:
f(0) = f(-0) = -f(0)
But that means 2f(0) = 0, which only happens if f(0) = 0.
2006-09-11 19:35:16 · answer #1 · answered by wlfgngpck 4 · 0⤊ 0⤋
A function with a graph that is symmetric with respect to the origin is an odd function. A function is odd if and only if f(–x) = –f(x).
If x = 0, then f(0) = -f(0)
The only time A = -A is when A = 0
so f(0) = 0
2006-09-11 20:32:22 · answer #2 · answered by Puzzling 7 · 0⤊ 0⤋
f=1
1(0)=0
2006-09-11 19:16:05 · answer #3 · answered by isaac a 3 · 0⤊ 0⤋
Let's disprove it, shall we.
Take f(x) = 1/x
Clearly: f(x) = 1/x = -1/(-x) = -f(-x) so f is an odd function.
BUT: f(0) is not defined, hence the proposition is false.
2006-09-11 23:38:10 · answer #4 · answered by sabrina_at_tc 2 · 1⤊ 0⤋
i don't think f has to be odd even...
2006-09-11 19:01:22 · answer #5 · answered by Anonymous · 0⤊ 0⤋