# Let f : (– 1, 1) ® B, be a function defined by f (x) = 1 2 2 tan 1 x x – – , then f is both one – one and onto when B is the interval

Question:

Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^{2}}$, then $\mathrm{f}$ is both one – one and onto when $B$ is the interval

1. $\left(0, \frac{\pi}{2}\right)$

2. $\left[0, \frac{\pi}{2}\right)$

3. $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

4. $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year 2005

Solution:

### Related Questions

• Let $R_{1}$ and $R_{2}$ be two relations defined as follows :

$R_{1}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \in Q\right\}$ and

$R_{2}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \notin Q\right\}$, where $Q$ is the set of all rational numbers. Then :

View Solution

• The domain of the function $f(x)=\sin ^{-1}\left(\frac{|x|+5}{x^{2}+1}\right)$ is $(-\infty,-a] \cup[a, \infty]$. Then $a$ is equal to :

View Solution

• If $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :

View Solution

• If $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :

View Solution

• Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x}{1+x^{2}}, x \in R$. Then the range of $f$ is :

View Solution

• The domain of the definition of the function $f(x)=\frac{1}{4-x^{2}}+\log _{10}\left(x^{3}-x\right)$ is:

View Solution

• The range of the function $f(x)=\frac{x}{1+|x|}, x \in R$, is is

View Solution

• The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is

View Solution

• Domain of definition of the function $f(x)=\frac{3}{4-x^{2}}+\log _{10}\left(x^{3}-x\right)$, is

View Solution

• Let $[t]$ denote the greatest integer $\leq t$. Then the equation in $x,[x]^{2}+2[x+2]-7=0$ has :

View Solution

error: Content is protected !!
Download App