## Precalculus: Mathematics for Calculus, 7th Edition

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