Determine the composite mapping $$ f \circ g $$ of the maps $$ f: \mathbb{R} \rightarrow \mathbb{R} $$ and $$ g: \mathbb{R} \rightarrow \mathbb{R} $$ are defined (a) $$ f(x)=\log \left(\frac{1+x}{1-x}\right) $$ and $$ g(x)=\frac{3 x+x^{3}}{1+3 x^{2}} $$ (b) $$ f(x)=\sin x $$ and $$ g(x)=x^{2} $$

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Lindsey Thornton · Accepted Answer

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

Determine the composite mapping \( f \circ g \) of the maps \( f: \mathbb{R} \rightarrow \mathbb{R} \) and \( g: \mathbb{R} \rightarrow \mathbb{R} \) are defined (a) \( f(x)=\log \left(\frac{1+x}{1-x}\right) \) and \( g(x)=\frac{3 x+x^{3}}{1+3 x^{2}} \) (b) \( f(x)=\sin x \) and \( g(x)=x^{2} \)

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Determine the composite mapping \( f \circ g \) of the maps \( f: \mathbb{R} \rightarrow \mathbb{R} \) and \( g: \mathbb{R} \rightarrow \mathbb{R} \) are defined (a) \( f(x)=\log \left(\frac{1+x}{1-x}\right) \) and \( g(x)=\frac{3 x+x^{3}}{1+3 x^{2}} \) (b) \( f(x)=\sin x \) and \( g(x)=x^{2} \)

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