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{f(x)=ln(1+x1−x),f:(−1,1)→Rg(x)=3x+x31+3x2,g:R→(−1,1)\large \begin{cases} f(x) = \ln \left( \dfrac{1+x}{1-x} \right), & \quad f : (-1,1) \to \mathbb{R} \\ g(x) = \dfrac{3x+x^3}{1+3x^2}, & \quad g : \mathbb{R} \to (-1,1) \end{cases}⎩⎪⎪⎨⎪⎪⎧f(x)=ln(1−x1+x),g(x)=1+3x23x+x3,f:(−1,1)→Rg:R→(−1,1)
For f(x)f(x)f(x) and g(x)g(x)g(x) as defined above, what is f∘g(x)f \circ g (x)f∘g(x) or f(g(x))f(g(x))f(g(x))?
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