Find the domain of the function f(x)=[tex]\sqrt{x^3-16x}[/tex] . What is the least value of x in the domain?

Least Value=

Respuesta :

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,  

  • Domain refers to all the possible sets of input values on the x-axis.

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.

ACCESS MORE
EDU ACCESS