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

x ∈ (-∞, -4] ∪ [ 4, ∞ )

Step-by-step explanation:

Given expression is,

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

That is,

= 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, ∞ )

step-by-step explanation: