Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=\sqrt{x^3-16x}[/tex]
We know that the domain of the function is the set of input or arguments for which the function is real and defined.
In other words,
Now, determine non-negative values for radicals so that we can sort out the domain values for which the function can be defined.
[tex]x^3-16x\ge 0[/tex]
as x³ - 16x ≥ 0
[tex]\left(x+4\right)\left(x-4\right)\ge \:0[/tex]
Thus, identifying the intervals:
[tex]-4\le \:x\le \:0\quad \mathrm{or}\quad \:x\ge \:4[/tex]
Thus,
The domain of the function f(x) is:
[tex]x\left(x+4\right)\left(x-4\right)\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-4\le \:x\le \:0\quad \mathrm{or}\quad \:x\ge \:4\:\\ \:\mathrm{Interval\:Notation:}&\:\left[-4,\:0\right]\cup \:[4,\:\infty \:)\end{bmatrix}[/tex]
And the Least Value of the domain is -4.