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!