Let f(x)= ( 6 ( 2 x ) ) for all x ∈ R and g(x)= 2 x for all x ∈ R . Let ( fog )( x )…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
Let \(f(x)=\sin \left(\frac{\pi}{6} \sin \left(\frac{\pi}{2} \sin x\right)\right)\) for all x ∈ R and \(g(x)=\frac{\pi}{2} \sin x\) for all x ∈ R. Let (fog)(x) denote f(g(x)) and (gof)(x) denote g(f(x)). Then which of the following is (are) true?
- There is an x
Answer
(D) There is an x ∈ R such that ( gof )( x ) = 1
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