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Let $a$, $b$ and $c$ be real numbers and consider that $f$ maps $\mathbb{R}$ to $\mathbb{R}$.

For what values of $a$, $b$ and $c$ is $f(x) = ax^2 + bx + c$ (i) one-to-one? (ii) onto?

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    It would be great if you could show us some of the work you've done. Have you considered what shape the graphs of the functions take for different values of $a,\ b$ and $c$?2012-11-19
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    I was thinking if a = 0 and b is not equal to zero, that is one case when f is both one-to-one and onto, but i couldn't figure out how to formulate the argument when a is not equal to zero. Also i tried to do an algebraic solution but ran out of ideas?2012-11-19

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