Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let f(x) = x 2 and g(x) = sin x for all x ∈ R. Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x), where (f o g) (x) = f(g(x)), is
A
± 
, n ∈ {0, 1, 2,....}
, n ∈ {0, 1, 2,....}
B
± 
, n ∈ {1, 2,....}
, n ∈ {1, 2,....}
C
+ 2n π , n ∈ {.....–2, –1, 0, 1, 2,....}
D
2n π , n ∈ {...., –2, –1, 0, 1, 2,....}
Text Solution
Verified by ExpertsThe correct answer is:
A
Sol. f(x) = x 2 ; g (x) = sin x ⇒ gof (x) = sin x 2 ⇒ gogof (x) = sin (sin x 2 )
⇒ (fogogof) (x) = (sin (sin x 2 )) 2 = sin 2 (sin x 2 )
Now sin 2 (sin x 2 ) = sin (sin x 2 ) ⇒ sin (sin x 2 ) = 0, 1
⇒ sin x 2 = n π , (4n+1) 
; 
⇒ sin x 2 = 0
⇒ x 2 = n π ⇒ x = 
; n ∈ W
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