f : Z Z given by f(x) = x^2 - Vidyadip

Question

$f : Z \rightarrow Z$ given by $f(x) = x^2$

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Answer

$f : Z \rightarrow Z$ is given by,
$f(x) = x^2$
It is seen that for $f(= 1) = f(1) = 1,$ but $-1\neq1.$
$\therefore f$ is not injective.
Now$, -2\in\text{Z}.$
But, there does not exist any element $\text{x}\in\text{Z}$ such that $f(x) = x^2 = -2$.
$\therefore f$ is not surjective.
Hence, function $f$ is neither injective but not surjective.

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