#### Answer

$D=\{x|x\leq\dfrac{1}{2}\}=(-\infty,\dfrac{1}{2}]$

#### Work Step by Step

$f(x)=\sqrt{1-2x}$
This function is undefined when the expression inside the root is a negative number. To find the domain, let's solve the following inequality:
$1-2x\geq0$
$2x\leq1$
$x\leq\dfrac{1}{2}$
All the numbers less than $\dfrac{1}{2}$, including it, are part of the domain of the function. This can be expressed as follows:
$D=\{x|x\leq\dfrac{1}{2}\}=(-\infty,\dfrac{1}{2}]$