Determine the value of p for the function f(x) = a/(x+p) + q, whose domain is (-infinity; 1) (1; infinity).

The domain of the function $f(x) = \frac{a}{x+p} + q$ is given as $(-\infty; 1) \cup (1; \infty)$. This indicates that there is a vertical asymptote at $x=1$.
For a rational function of this form, the vertical asymptote occurs when the denominator is zero, i.e., $x+p = 0$.
Therefore, $x = -p$.
Comparing this with $x=1$, we have $-p = 1$, which means $p = -1$.

A line of symmetry