Question #2169

The function f : R to R+ U {0} , f(x) : x^2 is one-one
but not onto.
State true or false, why?

Expert's answer

R to R_{+} : x^{2} - it's the part of parabola for positive x, it's one-to-one, since if f(x_{1}) = f(x_{2}), x_{1}=x_{2} and x^{2} is onto (surjective): for all x>=0 there is such y, that y = f(x).

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