#12
求所有函數\(f(x)\)，對任意實數\(x\)，\(|\;x|\;\ne 1\)，滿足\(\displaystyle f\left(\frac{x-3}{x+1}\right)+f\left(\frac{3+x}{1-x}\right)=x\)，則\(f(x)=\) 。
[解答]
自問自答 = ="|||
設 t = x-3 / x+1 => x = -t-3 / t-1 => f(t) + f( t-3 / t+1) = -t-3 / t-1
設 t = 3+x / 1-x => x = t-3 / t+1 => f(-t-3 / t-1) + f(t) = t-3 / t+1
兩式相加: 2f(x) + x = -8x / x^2 -1
f(x) = x^3+7x / 2-2x^2
