Sets Relations And Functions Question 51
Question: The range of $ f(x)=si{n^{-1}}(\sqrt{x^{2}+x+1}) $ is
Options:
A) $ ( 0,\frac{\pi }{2} ] $
B) $ ( 0,\frac{\pi }{3} ] $
C) $ [ \frac{\pi }{3},\frac{\pi }{2} ] $
D) $ [ \frac{\pi }{6},\frac{\pi }{3} ] $
Show Answer
Answer:
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} $
BETA
