Question

Range of $f\left(X\right)=co{s}^{-1}\left(\frac{x^2+x+1}{x^4+1}\right)$ is

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

Answer 1

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

Let $g\left(x\right)=\frac{x^2+x+1}{x^4+1}$
$\Rightarrow 0<g\left(x\right)\le 1$
So range of f(x) is $[0,\frac{\pi }{2})$