Question

已知f(x+1/x-1)=3f(x)-2x,求f(x)

Answer 1

设t=(x+1)/(x-1)

则x=(t+1)/(t-1)

f(t)=3f(t+1/t-1)-2(t+1)/(t-1)

即f(x)=3f(x+1/x-1)-2(x+1)/(x-1)

联立原式,消去f（x+1/x-1)

f(x)=3x/4+(x+1)/4(x-1)