Question

graphing the cube root function quick
what is the domain of $g(x) = -sqrt3{x} + 5$? (1 point)
\\(\circ\\) $0 \leq y \leq \infty$
\\(\circ\\) $-\infty \leq y \leq \infty$
\\(\circ\\) $0 < x < \infty$
\\(\circ\\) $-\infty < x < \infty$

Explanation:

Step1: Recall Cube Root Domain

The cube root function \( \sqrt[3]{x} \) is defined for all real numbers \( x \), since we can take the cube root of any real number (positive, negative, or zero).

Step2: Analyze the Given Function

The function \( g(x) = -\sqrt[3]{x} + 5 \) involves a cube root of \( x \). There are no restrictions on \( x \) here (unlike square roots, which require non - negative radicands), so \( x \) can be any real number. The domain of a function is the set of all possible input values (\( x \)-values), so the domain of \( g(x) \) is all real numbers, which is represented as \( -\infty < x < \infty \).

Answer:

\( -\infty < x < \infty \) (the last option: \( -\infty < x < \infty \))