Given the function $f(x) = \left\{ \begin{array}{lll} \frac{x-1}{x^{2}-1} & \text{if} & x < 1, x \neq -1 \\ \frac{x^{2}+1}{4x} & \text{if} & x \geq 1 \end{array} \right.$, find:\ a) (0.5 points) Calculate $f(0)$ and $(f \circ f)(0)$.\ b) (1.25 points) Study the continuity and differentiability of $f(x)$ at $x = 1$ and determine if there exists a relative extremum at that point.\ c) (0.75 points) Study its asymptotes.