# Math Help - Inverse problem

1. ## Inverse problem

Find the inverse of f(x) = x/(sqrt(x^2+7)

This is what I did so far:
I switched the variables.
y = x/(sqrt(x^2+7))
Switch x and y,
x = y/(sqrt(y^2+7))
Square both sides,
x^2 = y^2/(y^2+7)
x^2y^2+7x^2 = y^2
Then I got the wrong answer, so I stopped here.

I was told to go on like this, which is the answer.
Though somehow it just went to 7x^2 and a 1-x^2 came along.
Like how did they do that?

y^2 = 7x^2/(1-x^2)
y = ±[7x^2/(1-x^2)]^(1/2)

Can someone explain or show in another way?
Thanks!

2. ## Re: Inverse problem

Originally Posted by Chaim
Find the inverse of f(x) = x/(sqrt(x^2+7)

This is what I did so far:
I switched the variables.
y = x/(sqrt(x^2+7))
Switch x and y,
x = y/(sqrt(y^2+7))
Square both sides,
x^2 = y^2/(y^2+7)
x^2y^2+7x^2 = y^2
You are correct up to this point. You said that "then I got the wrong answer", so, did you attempt to solve for y? What did your attempt look like? Perhaps if you show some of your work, we can help you and explain where the $1-x^2$ expression came from.