i have the following function: $f:\mathbb{Z}\rightarrow\mathbb{Z}$ , $f(n)=n(n+1)$
Calculate: $f^{-1}({1})$, $f^{-1}({2})$, $f^{-1}(\mathbb{{N}})$ (Natural numbers)
for the first one i got the empty set, for the second one I got the solution $\{-2,1\}$.
However for the last one I couldn't really find a solution. If i put in an even number, the result is also even. If i put in an uneven number, I also get an even result. Therefore not every natural number is in the solution.
Where am I making a mistake here?
edit: can't really make it format right. my bad! but its supposed to be the set that contains all natural numbers, not only natural numbers