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]
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