Range of 1/[root(x^2-4)]

Answer 1

you need x^2-4 > 0 for the domain
So the range is y > 0, or (0,∞)

Answer 2

I got the x in terms of y
And its y=root[(1+4y^2)/y^2]
Its range should not be (- infinity ,+ infinity)

Answer 3

Sorry its
x=root[(1+4y^2)/y^2]
f^-1(y)=root[(1+4y^2)/y^2]
f^-1(x)=root[(1+4x^2)/x^2 ]
Where (1+4x^2)/x^2>=0
This inequality is true for any real values of x. So, its range should not be (- infinity ,+ infinity)

Kindly check my solution again