Find the inverse of f(x)

[superevilcube]

I need to find the inverse of the following function. I think I am on the right track, so I wills how my work.

\(\displaystyle f(x)=\L \frac{x}{sqrt{x^2+7}}\)

I then switched out the variables and began to solve for \(\displaystyle y\)

\(\displaystyle x = \L \frac{y}{sqrt{y^2+7}}\)

\(\displaystyle x{sqrt{y^2+7}} = y\)

\(\displaystyle x^2(y^2+7) = y\)

\(\displaystyle x^2y^2+7x^2 = y\)

\(\displaystyle x^2y^2 = y-7x^2\)

\(\displaystyle x^2y^2-y = -7x^2\)

\(\displaystyle y(x^2y-1) = -7x^2\)

Am I on the right track? If so, what do I do next? (I'm completely stumped).

I know the answer is the following, so that's what I think I'm on the right tract:

\(\displaystyle f^-^1(x)=\L \frac{{sqrt{7}}x}{sqrt{1-x^2}}\) , -1< x <1

 

[pka]

In the third line you missed the square on the y.

 

[superevilcube]

Thanks! (I hate it when you make little mistakes like that, it screws up the whole problem!)