If f: R rightarrow R and g: R^{+} rightarrow | vedclass

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(C) Given,$g\{f(x)\}=|\sin x|$ and $f\{g(x)\}=(\sin \sqrt{x})^2$. Let us test the option $f(x)=\sin ^2 x$ and $g(x)=\sqrt{x}$. First,calculate $f\{g(x

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$f(x)=\sin ^2 x, g(x)=\sqrt{x}$

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(C) Given,$g\{f(x)\}=|\sin x|$ and $f\{g(x)\}=(\sin \sqrt{x})^2$. Let us test the option $f(x)=\sin ^2 x$ and $g(x)=\sqrt{x}$. First,calculate $f\{g(x)\}$: $f\{g(x)\} = f(\sqrt{x}) = \sin ^2(\sqrt{x}) = (\sin \sqrt{x})^2$. This matches the given condition. Next,calculate $g\{f(x)\}$: $g\{f(x)\} = g(\sin ^2 x) = \sqrt{\sin ^2 x} = |\sin x|$. This also matches the given condition. Therefore,the correct choice is $f(x)=\sin ^2 x$ and $g(x)=\sqrt{x}$.

If $f: R \rightarrow R$ and $g: R^{+} \rightarrow R$ are such that $g\{f(x)\}=|\sin x|$ and $f\{g(x)\}=(\sin \sqrt{x})^2$,then a possible choice for $f$ and $g$ is

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