Relations Question 8
Question: The range of the function f defined by $ f(x)=[ \frac{1}{\sin { x }} ] $ (where [.] and $ { . } $ , respectively, denote the greatest integer and the fractional part functions) is
Options:
A) I, the set of integers
B) N, the set of natural numbers
C) W, the set of whole numbers
D) $ { 1,2,3,4…. } $
Show Answer
Answer:
Correct Answer: D
Solution:
Since $ {x}\in [0,1),sin{x}\in (0,sin1) $ as $ f(x) $ is defined if $ \sin {x}\ne 0, $
i.e., $ \frac{1}{\sin {x}}\in ( \frac{1}{\sin 1},\infty ) $
Or $ [ \frac{1}{\sin {x}} ]\in {1,2,3…} $
Note that $ 1<\frac{\pi }{3} $ or $ \sin 1<\sin \frac{\pi }{3}=0.866 $ or $ \frac{1}{\sin 1}>1.155. $
BETA
