Which of the following does not represent the domain of the function \( g(x)=-\sqrt[3]{x}+5 \) ? Option \#1: \( (-\infty, \infty) \) Option \#2:- \( -\infty

Ask by Johnson Bolton. in the United States

Jan 23,2025

The best answer is Option \# 3. While both Option \#1 and Option \#2 effectively describe the full domain of the function \( g(x) = -\sqrt[3]{x} + 5 \), which is all real numbers, Option \#3 includes an incorrect use of the interval notation by adding brackets that imply a closed interval including infinity, which is not possible. In this function, since the cube root function can take any real number as input, the domain is indeed all real numbers. Therefore, you can plug in any value for \( x \) without restriction!