Question:

Let \( g(x) \) be a polynomial, of degree one & \( f(x) \) be defined by \( f(x) = \begin{cases} g(x), & x \leq 0 \ \frac{1+x}{2+x}, & x > 0 \end{cases} \). Find the continuous function \( f(x) \) satisfying \( f'(1) = f(-1) \).