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Functions question

2011 · Shift 2 · Q34
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  5. /2011 · Shift 2 · Q34

Functions question

2011 · Shift 2 · Q34

JEE AdvancedMathematicsFunctionsMCQ+3 / −1
Let f(x) = x2 and g(x) = sin x for all x ∈\in∈ R. Then the set of all x satisfying (f∘g∘g∘f)(x)=(g∘g∘f)(x)(f \circ g \circ g \circ f)(x) = (g \circ g \circ f)(x)(f∘g∘g∘f)(x)=(g∘g∘f)(x), where (f∘g)(x)=f(g(x))(f \circ g)(x) = f(g(x))(f∘g)(x)=f(g(x)), is
  1. A
    ±nπ, n∈{0,1,2,....}\pm \sqrt {n\pi } ,\,n \in \{ 0,1,2,....\}±nπ​,n∈{0,1,2,....}
  2. B
    ±nπ, n∈{1,2,....}\pm \sqrt {n\pi } ,\,n \in \{ 1,2,....\}±nπ​,n∈{1,2,....}
  3. C
    π2+2nπ, n∈{.....,−2,−1,0,1,2,....}{\pi \over 2} + 2n\pi ,\,n \in \{ ....., - 2, - 1,0,1,2,....\}2π​+2nπ,n∈{.....,−2,−1,0,1,2,....}
  4. D
    2nπ,n∈{.....,−2,−1,0,1,2,....}2n\pi ,n \in \{ ....., - 2, - 1,0,1,2,....\}2nπ,n∈{.....,−2,−1,0,1,2,....}
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