MathematicsMedium179×since 2002Q4162Let g(x)g(x)g(x) be a linear function and f(x)={g(x),x≤0(1+x2+x)1x,x>0f(x)=\left\{\begin{array}{cl}g(x) & , x \leq 0 \\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}} & , x>0\end{array}\right.f(x)={g(x)(2+x1+x)x1,x≤0,x>0, is continuous at x=0x=0x=0. If f′(1)=f(−1)f^{\prime}(1)=f(-1)f′(1)=f(−1), then the value g(3)g(3)g(3) isAloge(49)−1\log _e\left(\frac{4}{9}\right)-1loge(94)−1B13loge(49e1/3)\frac{1}{3} \log _e\left(\frac{4}{9 e^{1 / 3}}\right)31loge(9e1/34)Cloge(49e1/3)\log _e\left(\frac{4}{9 e^{1 / 3}}\right)loge(9e1/34)D13loge(49)+1\frac{1}{3} \log _e\left(\frac{4}{9}\right)+131loge(94)+1Check answerSkip