Solve y=f(x): Range of f & Verify x in terms of y

[physstudent1]

Homework Statement

Solve y=f(x) for x. What is the range of f? Your expression for x in terms of y may be helpful to verify your statement.

f(x) = sqrt(x/(4-x))

Homework Equations

The Attempt at a Solution

I solved for x and got x = 4y^2/(1+y^2). I would like to know if this is correct or not also would the range of this be the domain of the original function because we had to find the domain in an earlier part of the question.

 

[D H]

$x=4y^2/(1+y^2)$ is correct. What are the range and domain of this mapping? You should be able to see that this does not match the domain and range of the original function.

 

[physstudent1]

i thought that doing this would give me the inverse though and that with an inverse the domain and range are switched

 

[D H]

Two numbers satisfy the equation $y^2=x$ for positive x. Only one of these two numbers satisfies $y=\sqrt x$.

 

[physstudent1]

ah I see thank's a ton :). Would the domain be all real positive numbers and 0; and would the range be all reals ?

 

[D H]

Correct. BTW, a shorter way to say "all real positive numbers and 0" is "the non-negative reals".

 

[physstudent1]

thank you DH you're helping me a ton tonight.