To determine the domain of the function [tex]\( f(x) = x^3 \)[/tex], we need to identify all the possible values that [tex]\( x \)[/tex] can take without causing any undefined behavior in the function.
Here, [tex]\( f(x) = x^3 \)[/tex] is a polynomial function, specifically a cubic function.
Polynomial functions are defined for all real numbers because they do not have denominators, square roots, logarithms, or any other operations that could cause the function to be undefined for certain values of [tex]\( x \)[/tex].
Therefore, there are no restrictions on the values of [tex]\( x \)[/tex]. This means that [tex]\( x \)[/tex] can be any real number.
In interval notation, the set of all real numbers is represented as:
[tex]\[
(-\infty, \infty)
\][/tex]
So, the domain of the function [tex]\( f(x) = x^3 \)[/tex] is:
[tex]\[
(-\infty, \infty)
\][/tex]
