Step-by-Step Solution for Inverse of a Quadratic Function

[crm08]

Homework Statement

The original problem asks for the inverse of f(x) = (1-sqrt(x))/(1+sqrt(x))
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Homework Equations

The Attempt at a Solution

When I swap the variables and get to x = (1-sqrt(y))/(1+sqrt(y)), I am having problems showing the steps to get to my final answer, which I know by solving with my 89 is Y = (x-1)^2/(x+1)^2, could you help me with the steps in between.

 

[NoMoreExams]

First solve for sqrt(y), can you do that?

 

[crm08]

having trouble solving for sqrt(y), I know I'll have to do the subtraction before I can square both sides by looking at the answer, that's what is throwing me off, should I be trying to split the fraction into multiple fractions first?

 

[NoMoreExams]

Multiply both sides by 1 + sqrt(y), then move everything with sqrt(y) on one side and everything without on the other, what do you get?

 

[crm08]

i got (x)(sqrt(y) + sqrt(y) = 1 - x, or should I not be distributing the x?

 

[crm08]

never mind I see it now, thanks for your help

 

[NoMoreExams]

OK Good