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Determine the values of the variable for which the expression is defined as a real number. (enter your answer using interval notation.) square root of x^2 − 16

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x² must be no smaller than 16 because you can't take the square root of negative numbers (yet!). so x must be contained in the interval (4, infinity)

Answer:

x ∈ (-∞, -4] ∪ [ 4, ∞ )

Step-by-step explanation:

Given expression is,

[tex]\sqrt{x^2 -16}[/tex]

For being a real number the value inside the square root must be positive or zero,

That is,

[tex]\sqrt{x^2 -16}[/tex] = real number,

If x² - 16 ≥ 0

∵ square of a real number is always positive, ( however number is negative )

Thus, x² - 16 ≥ 0 is possible if x is 4, -4, greater than 4 or less than -4,

I.e. x ∈ (-∞, -4] ∪ [ 4, ∞ )

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