In which of the function is onto defined in R R.

MCQ

In which of the function is onto defined in $R \rightarrow R$.

A
$f(x)=|x|$
B
$f(x)=e^{-x}$
✓
$f(x)=x^3$
D
$f(x)=\sin x$.

✓

Answer

Correct option: C.

$f(x)=x^3$

(C) $
f(x)=x^3
$
Here $f: R \rightarrow R$
and$
f(x)=x^3
$
Suppose $y \in R$ co-domain if possible then pre image of $y$ in domain R is $x$.$
\begin{array}{c}
f(x)=y \\
\Rightarrow y=x^3 \therefore x=(y)^{1 / 3} \in R \forall y \in R
\end{array}
$
So, every value $y$ has exist pre image in domain R .
So, $f$ is onto function.

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 Relations and Functions→Relations and Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The binary operation $\times$ defined on $N$ by $a \times b = a + b + ab$ for all $a, b \in N$ is:

→

If $y=e^{\frac{1}{2} \log \left(1+\tan ^2 x\right)}$, then $\frac{d y}{d x}$ is equal to

→

The system of equations $4x + y - 2z = 0\ ,\ x - 2y + z = 0$ ; $x + y - z =0 $ has

→

$a \times (b \times c)$ is coplanar with

→

Lef $f:(0, \pi) \rightarrow R$ be a function given by

$f(x)=\left\{\begin{array}{cc}\left(\frac{8}{7}\right)^{\frac{\tan 8 x}{\tan 7 x}}, & 0 < x < \frac{\pi}{2} \\ a-8, & x=\frac{\pi}{2} \\ (1+\mid \cot x)^{\frac{b}{a}|\tan x|}, & \frac{\pi}{2} < x < \pi\end{array}\right.$

Where $a, b \in Z$. If $f$ is continuous at $x=\frac{\pi}{2}$, then $\mathrm{a}^2+\mathrm{b}^2$ is equal to ..........

→

Which of the following functions from $\text{A}=\{\text{x}:-1\leq\text{x}\leq1\}$ to it self are bijections?

→

The altitude of a cone is $20\ cm$ and its semi $-$ vertical angle is $30^\circ .$ If the semi $-$ vertical angle is increasing at the rate of $2^\circ $ per second, then the radius of the base is increasing at the rate of :

→

If $S$ is the sum of the first $10$ terms of the series $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\tan ^{-1}\left(\frac{1}{21}\right)+\ldots$ then $\tan ( S )$ is equal to

→

Consider the matrix $f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$

Given below are two statements:

Statement I: $f(-x)$ is the inverse of the matrix $f(x)$.

Statement II: $f(x) f(y)=f(x+y)$.