Question

given the function $f(x) = 4x^3 - x$, which of the following describes its domain? (1 point)
○ $(-infty, infty)$
○ $(4, infty)$
○ $(-4, 4)$
○ $(-infty, 4)$

Explanation:

Step1: Identify Function Type

The function \( f(x) = 4x^3 - x \) is a polynomial function (cubic polynomial).

Step2: Recall Domain of Polynomials

The domain of any polynomial function (including linear, quadratic, cubic, etc.) is all real numbers, because there are no restrictions (like division by zero, square roots of negative numbers) on the input \( x \) for polynomials. In interval notation, all real numbers are represented as \( (-\infty, \infty) \).

Answer:

\( (-\infty, \infty) \) (the first option)