Question

graphing the cube root function practice
complete this assessment to review what youve learned. it will not count toward your gra
which of the following does not represent the domain of the function $g(x) = -sqrt3{x} + 5$?
option #1:$(-infty, infty)$
option #2:$-infty < x < infty$
option #3:$-infty, infty$
(1 point)

Explanation:

Step1: Recall domain of cube root function

The cube root function \( \sqrt[3]{x} \) has a domain of all real numbers, since we can take the cube root of any real number (positive, negative, or zero). So for \( g(x) = -\sqrt[3]{x} + 5 \), the domain is all real numbers.

Step2: Analyze interval notations

• Option #1: \( (-\infty, \infty) \) is the interval notation for all real numbers (open interval, since \( \infty \) is not a real number to include).
• Option #2: \( -\infty < x < \infty \) is the inequality notation for all real numbers, meaning \( x \) can be any real number.
• Option #3: \( [-\infty, \infty] \) is incorrect. Interval notation using square brackets implies including the endpoints, but \( \infty \) and \( -\infty \) are not real numbers and cannot be "included" in the interval. So this does not represent the domain.

Answer:

Option #3: \([-\infty, \infty]\)