I have $$f(x)=\begin{cases}k\cot(sx),&x<pa<qa\\ k\cot(s[x-b]),&x>qa>pa\end{cases}$$ I have to find $f(x)$ for $pa<x<qa$, given $s(a-b)=\pi$.
$p,q$ are any real nos.
Do I just say that $f(x)$ for this region is the same as equivalence of the two mentioned above?
$a$ is the length of the concerned complete region and $b$ is a constant whose value is defined from the above equation.
I also require the three functions to be continuous in [x, a]