FunctionHard
Question
Identify the statement(s) which is/are incorrect ?
Options
A.the function f(x) = cos (cos-1 x) is neither odd nor even
B.the fundamental period of f(x) = cos (sin x) + cos (cos x) is π
C.the range of the function f(x) = cos (3 sin x) is [- 1, 1]
D.none of these
Solution
(A) f(x) = cos (cos-1 x)
= x, x ∈ [-1, 1] odd function
(B) f(x + π) = cos (sin (x + π)) + cos (cos (x + π))
f(x + π) = cos (sin x) + cos (cos x) = f(x)
f
= cos 
+ cos 
= cos (cos x) + cos (sin x)
= f(x)
fundamental period = π/2
(C) f(x) = cos (3 sin x), x ∈ [-1, 1]
- 3 ≤ 3 sin x ≤ 3
cos (3 ) ≤ cos (3 sin x) ≤ 1
∴ Range is [cos (3 ), 1]
= x, x ∈ [-1, 1] odd function
(B) f(x + π) = cos (sin (x + π)) + cos (cos (x + π))
f(x + π) = cos (sin x) + cos (cos x) = f(x)
f
= cos + cos = cos (cos x) + cos (sin x)
= f(x)
fundamental period = π/2
(C) f(x) = cos (3 sin x), x ∈ [-1, 1]
- 3 ≤ 3 sin x ≤ 3
cos (3 ) ≤ cos (3 sin x) ≤ 1
∴ Range is [cos (3 ), 1]
Create a free account to view solution
View Solution FreeMore Function Questions
If S be the set of all triangles and f : S → R+, f (ᐃ) = Area of ᐃ, then f is -...Range of the function f(x) = cos (K sin x) is [-1 , 1] , then the least positive integral value of K will be -...The range of 5 cos x − 12 sin x + 7 is -...If q2 - 4 p r = 0, p > 0, then the domain of the function f(x) = log (p x3 + (p + q) x2 + (q + r) x + r) is:...If f (x) = sin (x)(where [ . ] denotes the greatest integer function) has π as its fundamental period, then -...