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

Question

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

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Answer

$f: R \rightarrow R$ is given by,
$f(x) = x^2$
It is seen that $f(-1) = f(1) = 1,$ but $-1\neq1.$
$\therefore$ f is not injective.
Now, $-2\in\text{R}.$ But, there does not exist any element $\text{x}\in\text{R}$ such that $f(x) = x^2 = -2.$
$\therefore f$ is not surjective.
Hence, function $f$ is neither injective nor surjective.

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