gIven:
[tex]\begin{gathered} \: f\mleft(x\mright)\: =\: \sqrt[]{x^2+4} \\ g\mleft(x\mright)=-\: 2x+1 \end{gathered}[/tex]Find the domain of
[tex]\frac{f\left(x\right)}{g\left(x\right)}[/tex]to solve,
[tex]\frac{f\left(x\right)}{g\left(x\right)}=\frac{\sqrt{x^2+4}}{-2x+1}[/tex]The domain of the above function is,
The undefined points are,
[tex]\begin{gathered} x<\frac{1}{2} \\ \: x>\frac{1}{2} \end{gathered}[/tex]the answer is
In interval notation,
[tex](-\infty\: ,\: \frac{1}{2})\cup(\frac{1}{2},\: \infty\: )[/tex]