The function f : R R, f(x) = x^2 is: - Vidyadip

MCQ

The function $f : R \rightarrow R, f(x) = x^2$ is:

A
Injective but not surjective.
B
Surjective but not injective.
C
Injective as well as surjective.
✓
Neither injective nor surjective.

✓

Answer

Correct option: D.

Neither injective nor surjective.

Given function is $f : R \rightarrow R, f(x) = x^2$
If $f(x) = f(y)$ then
$x^2 = y^2$
$\Rightarrow \text{x}\pm\text{y}$
Hence, it is not one $-$ one or injective.
$f(x) = y$
$y = x^2$
$\text{x}=\pm\sqrt{\text{y}}$
But co $-$ domain is $R$.
Hence, it is not onto or surjective.

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