Question:
What is the range of the function?
What is the range of the function?
Options:
- a) [0, ¥)
- b) (0.5, ¥)
- c) [1, ¥)
- d) (-¥, 0.5]
- a) [0, ¥)
- b) (0.5, ¥)
- c) [1, ¥)
- d) (-¥, 0.5]
correct answer : b)
Explanation:
y = (1 – cos x)-1 =
1
1- cosx
= 1
2 2
2sin x
= 1
22
2cosec x
\
cosec x
2
¬ (- ¥, -1) È (1, ¥)
cosec2
2
x
¬ (1, ¥)
Þ 1
22
2cosec x
¬ (0.5, ¥)
Range = (0.5, ¥)
y = (1 – cos x)-1 =
1
1- cosx
= 1
2 2
2sin x
= 1
22
2cosec x
\
cosec x
2
¬ (- ¥, -1) È (1, ¥)
cosec2
2
x
¬ (1, ¥)
Þ 1
22
2cosec x
¬ (0.5, ¥)
Range = (0.5, ¥)