A rational function is defined as long as the denominator is never equal to zero. In our case,
[tex]\begin{gathered} 5x+11=0 \\ \Rightarrow5x+11-11=0-11=-11 \\ \Rightarrow5x=-11 \\ \Rightarrow\frac{1}{5}(5x)=\frac{1}{5}(-11)=-\frac{11}{5} \\ \Rightarrow x=-\frac{11}{5} \end{gathered}[/tex]
Then, the only value that indeterminates the function is x= -11/5
[tex]\text{domain(}f(x)\text{)=}\mleft\lbrace x\in\mathfrak{\Re }|x\ne-\frac{11}{5}\mright\rbrace=(-\infty,-\frac{11}{5})\cup(-\frac{11}{5},\infty)[/tex]
