Answer
The domain of the function $h\left( x \right)=\sqrt{8-2x}$ is $\left( -\infty,4 \right]$.
Work Step by Step
Consider the given function $h\left( x \right)=\sqrt{8-2x}$.
Note that this function involves the square root.
Since the square root of a negative real number is not defined, the expression written inside the square root sign must be non-negative.
This means that $8-2x\ge 0$
or $8\ge 2x$
or $x\le 4$
Therefore, the domain of the function $h\left( x \right)=\sqrt{8-2x}$ is $\left( -\infty,4 \right]$.
