Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Which of the following function are defined for all x
A
sin[x] + cos [x] ([x] denotes greatest integer ≤ x)
B
sec –1 (1 + sin 2 x)
C
tan (log x)
D
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,b,d)
sin[x] + cos[x] is defined for all x, since [x], sin θ , cos θ are always defined.
sin x is always defined and 1 + sin 2 x ≥ 1
⇒ sec –1 (1+ sin 2 x) is defined for all x
tan(log x) is not defined if logx = (2k + 1) 
Range of function cosx + cos 2x is 
put cos x = t, t ∈ [–1, 1] therefore
+ cos x + cos 2x > 0 for all x
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The function , where assumes its minimum value only at one point, if . Find .
2. If be two fixed positive integers such that for all real , then is a periodic function with …
3. The domain of the function , where the symbols have their usual meanings, is the set . Find nu…
If , then . Find .
, then is equal to . Find .
Let and be the roots of , then is equal to Find .