The function y = f(x), ,f ,: ,R R , given by f(x) = x | x | + x^3… - Vidyadip

MCQ

The function $y = f(x),\,f\,:\,R \to R$ , given by $f(x) = x\left| x \right| + {x^3}\left| x \right|$ is

A
one- one into
✓
one-one onto
C
many one into
D
many one onto

✓

Answer

Correct option: B.

one-one onto

b
$f(x)=\left\{\begin{array}{ll}{x^{4}+x^{2}} & {, x \geq 0} \\ {-x^{4}-x^{2},} & {x<0}\end{array}\right.$

$f^{\prime}(x) \geq 0,$ one - one function and range is $R.$

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 1. relation and function→1. relation and function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the shortest distance between the lines $L : \frac{ x -5}{-2}=\frac{ y -\lambda}{0}=\frac{ z +\lambda}{1}, \lambda \geq 0$ and $L _1: x +1= y -$ $1=4-z$ be $2 \sqrt{6}$. If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?

If $\text{A}=\begin{bmatrix}2&\lambda&-3\\0&2&5\\1&1&3\end{bmatrix},$ then $\text{A}^{-1}$ exists if:

$\lambda=2$
$\lambda\neq2$
$\lambda\neq-2$
$\text{None of these}$

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}a&{a\, + \,b}&{a\, + \,2b}\\{a\, + \,2b}&a&{a\, + \,b}\\{a\, + \,b}&{a\, + \,2b}&a\end{array}\,} \right|$ is

The value of $\int\limits_0^{\frac{\pi }{2}} {\sin \,8x\,\cot\, xdx\, + \int\limits_{ - \frac{\pi }{4}}^{\frac{\pi }{4}} {\ln \left( {\frac{{1 - \sin \,x}}{{1 + \sin \,x}}} \right)dx} } $ is equal to

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x+1\right) d x=$ _________.

The distance s metre covered by a body in $t$ seconds is given by $s = 3{t^2} - 8t + 5,$ the body will stop after

A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X = 3) = 2P(X = 1) and P(X = 2) = 0.3, then P(X = 0) is:

0.1
0.2
0.3
0.4

If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A - 2B is:

m × 3
3 × 3
m × n
3 × n

Let × be a binary operation on set of integers I, defined by a × b = a + b - 3, then find the value of 3 × 4.

2
4
7
6

The differential equation of the ellipse $\frac{\text{x}^{2}}{\text{a}^{2}}+\frac{\text{y}^{2}}{\text{b}^{2}}=\text{C}$ is:

$\frac{\text{y}''}{\text{y}'}+\frac{\text{y}'}{\text{y}}-\frac{1}{\text{x}}=0$
$\frac{\text{y}''}{\text{y}'}+\frac{\text{y}'}{\text{y}}+\frac{1}{\text{x}}=0$
$\frac{\text{y}''}{\text{y}'}-\frac{\text{y}'}{\text{y}}-\frac{1}{\text{x}}=0$
None of these.