Range of {sin ^{ - 1,}}left( {frac{{1 + {x^2}}}{{2 + {x^2}}}} right) is

English

Gujarati

Hindi

1.Relation and Function

normal

Range of ${\sin ^{ - 1\,}}\left( {\frac{{1 + {x^2}}}{{2 + {x^2}}}} \right)$ is

A

$\left[ { - \frac{\pi }{6},\frac{\pi }{6}} \right]$

B

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

C

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

D

$\left[ { \frac{\pi }{6},\frac{\pi }{2}} \right]$

Solution

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

$y=\sin ^{-1}(1)$ when $x \rightarrow \infty=\frac{\pi}{2}$

When $x=0 \Rightarrow y=\sin ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}$

Standard 12

Mathematics

Share

Similar Questions

If $f$ is an even function defined on the interval $(-5, 5),$ then four real values of $x$ satisfying the equation $f(x) = f\left( {\frac{{x + 1}}{{x + 2}}} \right)$ are

hard

(IIT-1996)

If $f(x) = \log \frac{{1 + x}}{{1 – x}}$, then $f(x)$ is

easy

Let $f(x)$ and $g(x)$ be two functions given by $f\left( x \right) = \frac{{2\sin \pi x}}{x}$ and $g\left( x \right) = f\left( {1 – x} \right) + f\left( x \right).$ If $g\left( x \right) = kf(\frac{x}{2})f\left( {\frac{{1 – x}}{2}} \right)$,then the value of $k$ is

normal

The minimum value of the function $f(x) = {x^{10}} + {x^2} + \frac{1}{{{x^{12}}}} + \frac{1}{{\left( {1\ +\ {{\sec }^{ – 1}}\ x} \right)}}$ is

normal

Suppose $f(x) = {(x + 1)^2}$ for $x \ge – 1$. If $g(x)$ is the function whose graph is the reflection of the graph of $f(x)$ with respect to the line $y = x$, then $g(x)$ equals

hard

(IIT-2002)