Question

Given that "f" is an ODD function and f(x+5)=f(x), f(1/3)=1. Find the value of f(14/3)

Answer 1

If f is odd, then f(-x)=-f(x), but I'm actually not sure how to advance here. Anyone have any ideas?

Answer 2

Does it assume the function is linear?

Answer 3

I think--and here I may be going out on a limb--that this problem excludes important info.

Answer 4

f(x+5)=f(x)
f(-x+5)=-f(x)
14/3=-1/3+5
that is all you need to solve this

Answer 5

@auora could you interact with us here please?

Answer 6

does giving me a medal mean that you got it?

Answer 7

To be honest, @TuringTest, I don't understand. Your second step lost me. I understand the rest now; common sense, although I missed it.

Answer 8

you want me to give show you then you mean?

Answer 9

Yes.

Answer 10

\[f(x+5)=f(x)\]\[f(\frac13)=1\]since f(x) is odd we can write\[f(-x+5)=f(-x)=-f(x)\]now since \(\frac{14}3=-\frac13+5\) we can write\[f(\frac{14}3)=f(-\frac13+5)=f(-\frac13)=-f(\frac13)=-1\]

Answer 11

I would have distribute the negative onto both terms of x+5. Why didn't you?

Answer 12

distributed

Answer 13

You can't really do that. There is no reason to think that -x=-(x+5), so making one argument negative does not make the other whole argument negative, just x. We also have no reason to thin that f(x+5) is odd.
The only thing we can do is let x=-x, changing nothing else, from which the above follows.

Answer 14

think*

Answer 15

let x=-y if you wish
would that imply that
f(x+5)=f(x)
leads to
f(-y-5)=f(-y)
no, it leads to
f(-y+5)=f(-y)

Answer 16

All, I think I understand now. Thanks for your help.

Answer 17

Anytime :)