Answer
$\left( -\infty, \dfrac{1}{4} \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=1-4x
,$ are all the values of $x$ for which the radicand is greater than or equal to $0.$ Express the answer in the interval notation.
$\bf{\text{Solution Details:}}$
Since the radicand should be greater than or equal to zero, then
\begin{array}{l}\require{cancel}
1-4x\ge0
\\\\
-4x\ge-1
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-4x\ge-1
\\\\
x\le\dfrac{-1}{-4}
\\\\
x\le\dfrac{1}{4}
.\end{array}
Hence, the domain is $
\left( -\infty, \dfrac{1}{4} \right]
.$
