Consider a function f: [ - 1,1 ] R where f(x) = _1 ^ - 1 x + _3 (… - Vidyadip

MCQ

Consider a function $f:\left[ { - 1,1} \right] \to R$ where $f(x) = {\alpha _1}{\sin ^{ - 1}}x + {\alpha _3}\left( {{{\sin }^{ - 1}}{x^3}} \right) + ..... + {\alpha _{(2n + 1)}}{({\sin ^{ - 1}}x)^{(2n + 1)}} - {\cot ^{ - 1}}x$ Where $\alpha _i\ 's$ are positive constants and $n \in N < 100$ , then $f(x)$ is

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

✓

Answer

Correct option: B.

one-one and into

b
$ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\alpha_{1}}{\sqrt{1-\mathrm{x}^{2}}}+ \frac{\alpha_{3}\left(3 \sin ^{-1} \mathrm{x}\right)^{2}}{\sqrt{1-\mathrm{x}^{2}}}+\ldots \ldots $

$+\frac{(2 \mathrm{x}+1)\left(\sin ^{-1} \mathrm{x}\right)^{2 n}}{\sqrt{1-\mathrm{x}^{2}}}+\frac{1}{\left(1+\mathrm{x}^{2}\right)} $

$\frac{\mathrm{d} y}{\mathrm{dx}}>0$ and function is one one

but range $\neq$ codomain

$\Rightarrow$ into fumction

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 STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as $"ARB$ iff there exists a non-singular matrix $P$ such that $PAP ^{-1}= B "$ Then which of the following is true?

The value of $\int_{}^{} {\frac{{{e^x}}}{{{e^x} + 1}}} \,dx$ is

Let $\vec{p}=2 \hat{i}+3 \hat{j}+k$ and $\vec{q}=\hat{i}+2 \hat{j}+k$ be two vectors. If $a$ vector $\vec{r}=(a \hat{i}+\beta \hat{j}+\gamma k)$ is perpendicular to each of the vectors $(\vec{p}+\bar{q})$ and $(\vec{p}-\vec{q})$, and $|\vec{r}|=\sqrt{3}$, then $|\alpha|+|\beta|+|\gamma|$ is equal to $.....$

The value of the integral, $\int_{1}^{3}\left[ x ^{2}-2 x -2\right] dx ,$ where $[x]$ denotes the greatest integer less than or equal to $x$, is :

The point of intersection of the line joining the points $(3, 4, 1)$ and $(5, 1, 6)$ and the $xy$ - plane is

The area bounded by the parabola $y^2=4 a x$ and $x^2=4 a y$ is :

What is the length of the longer diagonal of the parallelogram constructed on $5\vec{\text{a}}+2\vec{\text{b}}$ and $\vec{\text{a}}-3\vec{\text{b}}$ if it is given that $|\vec{\text{a}}|=2\sqrt{2},\big|\vec{\text{b}}\big|=3$ and the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ is $\frac{\pi}{4}$?

A bag contain $4$ white and $2$ black balls. Two balls are drawn at random. The probability that they are of the same colour is $ ...........$

If $\left|\begin{array}{lll}2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1\end{array}\right|+3=0$, then the value of $x$ is

If $\int\limits_0^1 {\,\,\frac{{\ell n\,x}}{{\sqrt {1\,\, - \,\,{x^2}} }}} dx$ $= k\, \int\limits_0^\pi {} ln \,(1 + \cos \,x)\, dx$ then the value of $k$ is :