Question

若函数f(x)=(x+a)/(x+b)的反函数f^-1(x)=(x+a)/(x+b),求a,b

Answer 1

y=(x+a)/(x+b)

xy+by=x+a

x(y-1)=a-by

x=(a-by)/(y-1)

f^-1(x)=(x+a)/(x+b)

=(a-bx)/(x-1)

a=任意实数 b=-1