Answer
domain: $\{x|x\le10\}$
Work Step by Step
The radicand of a square root should be non-negative. Thus, in the given function, $f(x)=\sqrt{10-x},$
\begin{align*}
10-x&\ge0
.\end{align*}
Using the properties of inequality, the inequality above is equivalent to
\begin{align*}
-x&\ge-10
\\
-1(-x)&\le(-10)(-1)
&(\text{reverse the inequality symbol})
\\
x&\le10
.\end{align*}
Hence, the permissible values of $x$, or the domain of $f(x)=\sqrt{10-x}$, are $\{x|x\le10\}$.
