Question

已知函数f（x）=（x-1除以x+1）²（x>1） 求 函数f（x）的反函数f

Answer 1

x>1,(x-1)/(x+1)>0;

y^0.5=(x-1)/(x+1)= 1-2/(x+1);

x=2/(1-y^0.5)-1=(1+y^0.5)/(1-y^0.5)

所以反函数f=(1+x^0.5)/(1-x^0.5) (x>0)