Answer to Question #2169 in Real Analysis for jenny

Question

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

State true or false, why?

Answer 1

R to R₊ : x² - it's the part of parabola for positive x, it's one-to-one, since if f(x₁) = f(x₂), x₁=x₂ and x² is onto (surjective): for all x>=0 there is such y, that y = f(x).