Question

Show that the reciprocal of an odd function is odd?

Answer 1

an odd function is defined as
f( -x ) = - f(x)

Answer 2

lets make a new function g(x) = 1 / f(x) , where f(x) is an odd function.
is g(x) an odd function?

Answer 3

I tried out several examples and they all tell me that it is an odd function. But I don't understand how I can prove that algebraically.

Answer 4

you need to show that g(-x) = - g(x) , where g(x) = 1/f(x) , and f is an odd function

Answer 5

g(-x) = 1/f(-x) and -g(x) = -1/f(x)

But since f(x) = f(-x) .. Ah those two are the same!

Answer 6

Thanks a lot! I understand it now :3

Answer 7

actually f(-x) = -f(x)

Answer 8

g(-x) = 1 / f(-x) = 1 / (-f(x)) = - 1/f(x) = - g(x)

but i figure thats what you meant

Answer 9

does that make sense?