Question

The range of the function $f\left(x\right)={\sin }^{-1}\left(\frac{x^2}{1+x^2}\right),x\in R$ is equal to :

• A. $(0,\frac{\pi }{2})$
• B. $[-\frac{\pi }{2},\frac{\pi }{2}]$
• C. $[0,\frac{\pi }{2})$
• D. $(-\frac{\pi }{2},\frac{\pi }{2})$

Answer 1

The correct option is C $[0,\frac{\pi }{2})$

$\frac{x^2}{1+x^2}=1-\frac{1}{1+x^2}$
$\because x^2\in [0,\infty )$
$\Rightarrow \frac{x^2}{1+x^2}\in [0,1)$
$\therefore$ Range of $f\left(x\right)\in [0,\frac{\pi }{2})$