1 Answer

Bijal · Answer 1 · 2022-06-26T13:50:03+0000

a) Since division by zero is undefined, we have that

$13-x\\eq0\Leftrightarrow x\\eq13$

In interval notation

$D=( -\infty ,13) \cup ( 13,\infty )$

b) Since a square root of a negative number is undefined over the Reals, we have that

$9+x\geqslant 0\Leftrightarrow x\geqslant -9$

In interval notation

$D=[-9,\infty )$

c)Since division by zero is undefined, we have that

$2x+1\\eq 0\Leftrightarrow 2x\\eq -1\Leftrightarrow x\\eq -(1)/(2)$

In interval notation

$D=\left( -\infty ,-(1)/(2)\right) \cup \left( -(1)/(2) ,\infty \right)$

d) Since a square root of a negative number is undefined over the Reals, we have that

$4x-3\geqslant 0\Leftrightarrow 4x\geqslant 3\Leftrightarrow x\geqslant (3)/(4)$

In interval notation

$D=\left[(3)/(4) ,\infty \right)$

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