Answer to Question #227043 in Complex Analysis for smi

Question #227043

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


1
Expert's answer
2021-08-20T04:51:56-0400
f(z)=1z1f(z)=\frac{1}{\sqrt{z-1}}

Domain for function


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

Thus we will have


z10,z10,z1.\sqrt{z-1}\neq 0,\newline z-1\neq 0,\newline z\neq 1.

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


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