a) Since division by zero is undefined, we have that
[tex]13-x\neq0\Leftrightarrow x\neq13[/tex]
In interval notation
[tex]D=( -\infty ,13) \cup ( 13,\infty )[/tex]
b) Since a square root of a negative number is undefined over the Reals, we have that
[tex]9+x\geqslant 0\Leftrightarrow x\geqslant -9[/tex]
In interval notation
[tex]D=[-9,\infty )[/tex]
c)Since division by zero is undefined, we have that
[tex]2x+1\neq 0\Leftrightarrow 2x\neq -1\Leftrightarrow x\neq -\frac{1}{2}[/tex]
In interval notation
[tex]D=\left( -\infty ,-\frac{1}{2}\right) \cup \left( -\frac{1}{2} ,\infty \right)[/tex]
d) Since a square root of a negative number is undefined over the Reals, we have that
[tex]4x-3\geqslant 0\Leftrightarrow 4x\geqslant 3\Leftrightarrow x\geqslant \frac{3}{4}[/tex]
In interval notation
[tex]D=\left[\frac{3}{4} ,\infty \right)[/tex]
