Let \( g(x) \) be a polynomial, of degree one \( \& f(x) \) be defined by \( f(x)=\left[\begin{a...

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Let \( g(x) \) be a polynomial, of degree one \( \& f(x) \) be defined by \( f(x)=\left[\begin{array}{cl}g(x), & x \leq 0 \\ \left(\frac{1+x}{2+x}\right)^{1 / x}, & x0\end{array}\right. \) and the continuous function \( f(x) \) satisfying \( f^{\prime}(1)=f(-1) \), then find \( g(x) \).
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