Relations Question 13
Question: The range of following function is $ f(x)=\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{…\infty }}}} $
Options:
A) $ [ 0,1 ] $
B) $ [ 0,1/2 ] $
C) $ [ 0,2 ] $
D) none of these
Show Answer
Answer:
Correct Answer: C
Solution:
Given
$ f(x)=\sqrt{(1-\cos x)(1-\cos x)\sqrt{(1-\cos x)\sqrt{…\infty }}} $
$ ={{(1-\cos x)}^{\frac{1}{2}}}{{(1-\cos x)}^{\frac{1}{4}}}{{(1-\cos x)}^{\frac{1}{8}}}…\infty $
$ ={{(1-\cos x)}^{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+…\infty }} $
$ ={{(1-\cos x)}^{\frac{1/2}{1-(1/2)}}} $
$ =1-\cos x $
Thus, the range of f(x) is [0, 2).
BETA
