Sets Relations And Functions Question 26
Question: The range of the function $f$ defined by $f(x)=\left[\frac{1}{\sin \{x\}}\right]$ (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) None of the above
Show Answer
Answer:
Correct Answer: B
Solution:
- [d] 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
