Centered at $x = 1$, the radius of convergence is $R = 2\sqrt{2}$.

Centered at $x = 1$, the radius of convergence is $R = \sqrt{8}$.

The singularities of $f(x)$ in the complex plane are at $x = -1 \pm 2i$.

Centered at $x = 0$, the radius of convergence is $R = 5$.