How do i extend f(x)= 1 - 1/(x+1) as an odd function. where 0<x?

Question

need major help here!

Answer 1

I'm assuming you mean its defined for x>0, and you want to define it for x<0 (as opposed to the other way around).

In that case, f(x) is odd if f(-x) = -f(x).
So for x<0, you want f(x) = -(1 - 1/(-x+1)), or 1/(-x+1) - 1. (just the negative of what it is for positive x, except you replace x by -x).

If you did mean you have it for x<0, you get exactly the same formula as above for x>0.

Answer 2

A property of odd functions is symmetry across the origin (0,0). All that means is you mirror the graph across the origin. Presuming you've already graphed the function for x < 0, that is.