Answer
For $x$ in the interval $[0,6]$
Work Step by Step
Complex (unreal) numbers are used when we cannot define a specific number; when it has no real definition. For example, even root of a negative number.
$\sqrt{6x-x^2}$
The expression above is defined as a real number when the expression inside square root is non-negative number, that is:
$6x-x^2\geq 0$
$x(6-x)\geq 0$
We can solve the inequality using intervals method.
We have two critical points (Those are the points where the expression is equal to $0$) and three intervals:
$x_1=0$
$x_2=6$
$(-\infty, 0]$ - Negative
$[0, 6]$ - Positive
$[6, +\infty)$ - Negative
Our solution is in the interval: $[0,6]$