A) \[\left( 0,\frac{\pi }{2} \right]\]
B) \[\left( 0,\frac{\pi }{3} \right]\]
C) \[\left[ \frac{\pi }{3},\frac{\pi }{2} \right]\]
D) \[\left[ \frac{\pi }{6},\frac{\pi }{3} \right]\]
Correct Answer: C
Solution :
[c] for the function to get defined, \[0\le {{x}^{2}}+x+1\le 1,\] but \[{{x}^{2}}+x+1\ge \frac{3}{4}\] Or \[\frac{\sqrt{3}}{2}\le \sqrt{{{x}^{2}}+x+1}\le 1\] Or \[\frac{\pi }{3}\le {{\sin }^{-1}}(\sqrt{{{x}^{2}}+x+1})\le \frac{\pi }{2}\]You need to login to perform this action.
You will be redirected in
3 sec