Question

Let f(x) = x² and g(x) = sin x for all x R. Then the set of all x satisfying fog x( ) = f g( (x)), is

(A)   ± √nπ, n∈ {0 1, , 2,...}

(B)   ± √nπ, n∈ {1, 2,...}

(C)  π/2 + 2nπ, n∈ {...,0 1, , 2,...}

(D)  2nπ,n∈{..., -2,-1,0,1,2, ...}

Answer 1

Correct option  (A)   ± √nπ, n∈ {0 1, , 2,...}

Explanation :

(f o g o g of (x) = sin² (sin x²) 

(g o g of) (x) = sin² (sin²)

Therefore,