y=(x^1/2)/(x-1)的反函数怎么求?

y=(x^1/2)/(x-1)的反函数怎么求?
y=(x^1/2)/(x-1)的反函数怎么求?

y=(x^1/2)/(x-1)的反函数怎么求?
(x-1)y=√x
xy-√x-y=0
(√x-y/2)²=y+y²/4
√x-y/2=√(y+y²/4)
√x=y/2+√(y+y²/4)
x=y²/4+y+y²/4+y√(y+y²/4)
反函数为y=x²/2+x+x√(x+x²/4)