F(x) = x² + 1/x + 1 Tentukan f¹(6)

[tex]$\begin{align}f(x)&=\frac{x^2+1}{x+1}\\y&=\frac{x^2+1}{x+1}\\y(x+1)&=x^2+1\\xy+y&=x^2+1\\x^2-xy&=y-1\\x^2-xy+\frac14y^2&=\frac14y^2+y-1\\\left(x-\frac12y\right)^2&=\frac14y^2+y-1\\x-\frac12y&=\sqrt{\frac14y^2+y-1}\\x&=\frac12y+\sqrt{\frac14y^2+y-1}\\f^{-1}(x)&=\frac12x+\sqrt{\frac14x^2+x-1}\\f^{-1}(6)&=\frac62+\sqrt{\frac{6^2}4+6-1}\\&=3\sqrt{9+6-1}\\&=\boxed{3+\sqrt{14}}\end[/tex]