Let f(x)=x2 and g(x)=sin⁡x fora ll x∈R. Then the set of all x satisfying (fogogof)(x)=(gogof)(x), where (fog)(x)=f(g(x)), is

∴ sin2⁡(sin⁡x2)=sin⁡(sin⁡x2)⇒sin⁡(sin⁡x2)[sin⁡(sin⁡x2)−1]=0⇒sin⁡x2=0⇒x2=nπ⇒x=±nπ,n∈{0,1,2,…}

Let f(x)=x2 and g(x)=sin⁡x fora ll x∈R. Then the set of all x satisfying (fogogof)(x)=(gogof)(x), where (fog)(x)=f(g(x)), is

∴ sin2⁡(sin⁡x2)=sin⁡(sin⁡x2)⇒sin⁡(sin⁡x2)[sin⁡(sin⁡x2)−1]=0⇒sin⁡x2=0⇒x2=nπ⇒x=±nπ,n∈{0,1,2,…}

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Let $f (x) = x^{2} and g (x) = \sin x for a ll x \in R$ . Then the set of all x satisfying $(f o g o g o f) (x) = (gog o f) (x)$ , where $(f o g) (x) = f (g (x))$ , is

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$\pm \sqrt{n π}, n \in {0, 1, 2, \dots .}$

$\pm \sqrt{n π}, n \in {1, 2, \dots}$

$\frac{π}{2} + 2 n π, n \in {\dots ., - 2, - 1, 0, 1, 2, \dots}$

$2 n π, n \in {\dots . . - 2, - 1, 0, 1, 2 \dots .}$

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$∴$ $\sin^{2} (\sin x^{2}) = \sin (\sin x^{2})$

$\Rightarrow \sin (\sin x^{2}) [\sin (\sin x^{2}) - 1] = 0 \Rightarrow \sin x^{2} = 0$

$\Rightarrow x^{2} = n π \Rightarrow x = \pm \sqrt{n π}, n \in {0, 1, 2, \dots}$

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Let f(x)=x2 and g(x)=sin⁡x fora ll x∈R. Then the set of all x satisfying (fogogof)(x)=(gogof)(x), where (fog)(x)=f(g(x)), is

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Let $f (x) = x^{2} and g (x) = \sin x for a ll x \in R$ . Then the set of all x satisfying $(f o g o g o f) (x) = (gog o f) (x)$ , where $(f o g) (x) = f (g (x))$ , is