Let $f(x)=1+\sqrt{x}$ and $g(x)=\frac{2 x}{x^2+1}$. Then

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Professor PC Thomas Classes · Answer

Intersecting $D_f = [0, \infty)$ with $D_g = \mathbb{R}$ leaves $[0,\infty)$. Range overlap uniquely isolates $\{1\}$.