I've been having trouble with determining if a function is one-to-one or onto. I found an example and would like to see how to go about this problem. If we have $f(x)=\frac{x}{x^2+1}$ where $f:\mathbb{Q}\rightarrow\mathbb{Q}$, is $f$ one-to-one? Onto? What about if $f:\mathbb{Z}\rightarrow\mathbb{Q}$?
Is $f:\mathbb{Q}\to\mathbb{Q}$ defined by $f(x)=\frac{x}{x^2+1}$ one-to-one? Onto?
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functions