Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If ƒ(x) = 
for x ∈ R, then ƒ(x) is continuous in -
A
(– ∞ , ∞ )
B
(– ∞ , ∞ ) – 
C
(– ∞ , ∞ ) – 
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
If |2 sin x| < 1, ƒ(x)
= 
= 
= x.
If | 2 sin x | = 1, ƒ(x) = 
= 
= 
x..
If | 2 sin x | > 1, ƒ(x) = 
= 
= 0.
Also, | 2 sin x | < 1, ⇒ | sin x | < 
⇒ 
< sin x < 
⇒ n π – 
< x < n π + 
,
| 2 sin x | = 1 ⇒ | sin x | = 
⇒ sin x = ± 
⇒ x = n π ± 
.
and |2 sin x| > 1 ⇒ | sin x | > 
⇒ sin x > 
or sin x < 
⇒ x = n π ± 
.
Thus, we have
ƒ(x) = 
The only doubtful points are x = n π ± 
.
Clearly, ƒ(x) is not continuous at x = n π ± 
.
∴ ƒ(x) is continuous in (– ∞ , ∞ )
– 
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