I was wondering, how can I show mathematically that f(x) = x2, defined for x <= 0 is one-to-one?
Can I do it like this:
If f(x) is one to one, then f(x1) = f(x2) if x1 = x2
(x1)2 = (x2)2
+-(x1) = +-(x2) but the domain is only defined for negative numbers so
-(x1) = -(x2)
therefore x1 = x2
or is this completely off?
(Sorry for the sloppy notation, I just thought it would be ok in this case, since the calculations are fairly short and simple)