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

✓

Answer

Correct option: B.

Surjective but not injective.

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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Functions→Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If one point on the vector 2i − 4j − k is (2, 1, 3), the other point is?

(−4, 3, 2)
(4, −3, −2)
(3, 2, 1)
(4, −3, 2)

Choose the correct answer from given four options in each of the Exercise:
The determinant $\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$ equals to:

The volume ( $V$ ) of the casted half cylinder will be

If $X$ is a random variable with probability distribution as given below:

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = X_i)$	$k$	$3k$	$3k$	$k$

The value of $k$ and its variance are:

The value of $\left|\begin{array}{rrr}\cos (\alpha+\beta) & -\sin (\alpha+\beta) & \cos 2 \beta \\ \sin \alpha & \cos \alpha & \sin \beta \\ -\cos \alpha & \sin \alpha & \cos \beta\end{array}\right|$ is independent of

The general solution of the dofferential equation $\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}+\text{y}}$ is:

$\text{e}^{\text{x}}+\text{e}^{-\text{y}}=\text{C}$
$\text{e}^{\text{x}}+\text{e}^{\text{y}}=\text{C}$
$\text{e}^{-\text{x}}+\text{e}^{\text{y}}=\text{C}$
$\text{e}^{-\text{x}}+\text{e}^{-\text{y}}=\text{C}$

$Q^+$ is the set of all positive rational numbers with the binary operation $^*$ defined by $\text{a}*\text{b}=\frac{\text{ab}}2\ \forall\text{ a, b}\in\text{Q}^+$. The inverse of an element $\text{a}\in\text{Q}^+$ is:

A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 22 green balls and one blue ball is

If $\text{P}(\text{A}\cup\text{B})=0.8$ and $\text{P}(\text{A}\cap\text{B})=0.3$ then $\text{P}(\overline{\text{A}})=\text{P}(\overline{\text{B}})=$

If $\text{f(x)}=\frac{1-\sin\text{x}}{(\pi-2\text{x})^2},$ when $\text{x}\neq\frac{\pi}{2}=\lambda$ then f(x) will be continuous function at $\text{x}=\frac{\pi}{2},$ where $\lambda=$

$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{2}$
none of these