Let [tex]y = F^{-1}(x)[/tex] and [tex]F(y) = x[/tex]
[tex]4y^2 - 1 = x\\4y^2 = x + 1\\y^2 = \frac{x + 1}{4}\\y = \sqrt{\frac{x + 1}{4}}\\f^{-1} = \sqrt{\frac{x + 1}{4}}[/tex]
