Question

2.设 f(x)=x/(2+x)2+xf[g(x)]=x/(1+2x) 1+2x,则g(x)=

Answer 1

问：2.设 f(x)=x/(2+x)2+xf[g(x)]=x/(1+2x) 1+2x,则g(x)=

答：您好亲亲~~已知 f(x) = x/(2+x)^2 + x，f[g(x)] = x/(1+2x) + 2x，求 g(x)。由已知，可得：f[g(x)] = g(x) / (2 + g(x))^2 + g(x)将 f[g(x)] 中的 g(x) 代入上式，得到：x/(1+2x) + 2x = g(x) / (2 + g(x))^2 + g(x)将等式两边通分，整理后可得：g(x) = (2 + g(x))^2 × [x/(1+2x) + 2x] / [1 + x/(1+2x) + 2x]化简上式，可得：g(x) = 4x / (1 + 4x)因此，f(x) = x/(2+x)^2 + x，f[g(x)] = x/(1+2x) + 2x，g(x) = 4x / (1 + 4x)