Given is a function f(x)= 1-x with 0 < x < 1 that should be extended on the interval [-1, 1] to get an odd function. Outside this interval it should be continued with a period of 2.
If it would be an even function, I would extend it to f(x) = 1-|x| as even functions are symmetric around the y-axis. Would this be correct?
Now I am not sure, how to extend it to an odd function. I remember that odd functions should be point symmetric around the origin, and I think that in this case it will stay the same: f(x)= 1-x. Can this be correct?