Originally Posted by

**Nora314** Hi everyone,

I was wondering, how can I show mathematically that f(x) = x^{2}, defined for x <= 0 is one-to-one?

Can I do it like this:

If f(x) is one to one, then f(x_{1}) = f(x_{2}) if x_{1} = x_{2}

so

(x_{1})^{2} = (x_{2})^{2}

+-(x_{1}) = +-(x_{2}) but the domain is only defined for negative numbers so

-(x_{1}) = -(x_{2})

therefore x_{1} = x_{2}

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)