Answer to Question #227043 in Complex Analysis for smi

Question

If f(z)= 1/\sqrt{|z-1} find the domain of definition of f.

Answer 1

$$f(z)=\frac{1}{\sqrt{z-1}}$$

Domain for function

$f(x)=\frac{g(x)}{h(x)}$ is equal to $h(x)\neq 0.$

Thus we will have

$$\sqrt{z-1}\neq 0,\newline z-1\neq 0,\newline z\neq 1.$$

Answer. $(-\infty,1)\bigcup (1,\infty).$