f: Z → Z given by f(x) = x2 - Vidyadip

Question

f: Z → Z given by f(x) = x²

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Answer

f: Z → Z is given by,
f(x) = x²
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) = x² = -2.
$\therefore$ f is not surjective.
Hence, function f is neither injective but not surjective.

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