Algebra/Calculus Problem?

Question

It’s been a while and I can’t remember how to do this.

Find f^-1(x). (the inverse function)

f(x) = (1-√x)/(1+√x)

I know the answer, but not how to get it.

The answer should be:

((1-x)/(1+x))^2

Answer 1

Set

y=(1-sqrt(x))/(1+sqrt(x))

=> y+y*sqrt(x)=1-sqrt(x)

=>(y+1)*sqrt(x)=1-y

=>sqrt(x)=(1-y)/(1+y)

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

Hence

f^(-1)(y)=((1-y)/(1+y))^2

as required.