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

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Homework Help Overview

The original problem asks for the inverse of the function f(x) = (1-sqrt(x))/(1+sqrt(x)). Participants are discussing the steps involved in finding the inverse, particularly focusing on the algebraic manipulation required after swapping the variables.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to solve for sqrt(y) after swapping the variables. There are discussions about the order of operations, such as whether to split fractions or distribute terms. Some participants express confusion about the necessary steps to isolate sqrt(y).

Discussion Status

There is an ongoing exchange of ideas with some participants providing guidance on how to manipulate the equation. One participant has indicated a moment of clarity regarding their understanding of the problem, suggesting that progress is being made.

Contextual Notes

Participants are navigating the algebraic complexities of the problem, with some expressing uncertainty about how to proceed with the manipulation of the equation. There is an emphasis on ensuring the correct order of operations is followed.

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Homework Statement



The original problem asks for the inverse of f(x) = (1-sqrt(x))/(1+sqrt(x))
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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.
 
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First solve for sqrt(y), can you do that?
 
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?
 
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?
 
i got (x)(sqrt(y) + sqrt(y) = 1 - x, or should I not be distributing the x?
 
never mind I see it now, thanks for your help
 
OK Good
 

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