Option a: [tex]-\infty<x<\infty[/tex] is the domain of the function
Explanation:
The function is [tex]y=\sqrt[3]{x-1}[/tex]
The domain of the function is the set of independent values for which the function is real and well defined.
The domain of the cube root of the function is the set of all real numbers. Because, it is possible for a cube root to have three negative values.
Writing the domain in interval notation, we have,
[tex](-\infty, \infty)[/tex]
Thus, the domain of a cube root function is [tex](-\infty, \infty)[/tex]
It can also be written as [tex]-\infty<x<\infty[/tex]
Hence, [tex]-\infty<x<\infty[/tex] is the domain of the function [tex]y=\sqrt[3]{x-1}[/tex]
Thus, Option a is the correct answer.
