Range of f(x) = sin^ -1 (x^2 + x +1) is - - Vidyadip

MCQ

Range of $f(x) = sin^{-1} (\sqrt {x^2 + x +1})$ is -

A
$\left[ {0,\frac{\pi }{6}} \right]$
B
$\left[ {\frac{\pi }{6},\frac{\pi }{4}} \right]$
C
$\left[ {\frac{\pi }{4},\frac{\pi }{3}} \right]$
✓
$\left[ {\frac{\pi }{3},\frac{\pi }{2}} \right]$

✓

Answer

Correct option: D.

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

d
$\sqrt{x^{2}+x+1} \in\left[\frac{\sqrt{3}}{2}, 1\right]$

$\therefore f(\mathrm{x}) \in\left[\frac{\pi}{3}, \frac{\pi}{2}\right]$

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