Question

Find the domain of the following rational function, using interval notation. Show all work Detailed step by step

Answer 1

A rational function is defined as long as the denominator is never equal to zero. In our case,

`\begin{gathered} 5x+11=0 \\ \Rightarrow5x+11-11=0-11=-11 \\ \Rightarrow5x=-11 \\ \Rightarrow(1)/(5)(5x)=(1)/(5)(-11)=-(11)/(5) \\ \Rightarrow x=-(11)/(5) \end{gathered}`

Then, the only value that indeterminates the function is x= -11/5

`\text{domain(}f(x)\text{)=}\mleft\lbrace x\in\mathfrak{\Re }|x\\e-(11)/(5)\mright\rbrace=(-\infty,-(11)/(5))\cup(-(11)/(5),\infty)`