State the domain of the function.
wequals=​h(u)equals=RootIndex 3 StartRoot u minus 3 EndRoot3u−3 

The given function is:

\[
w = h(u) = \sqrt[3]{u - 3}
\]

To determine the **domain** of this function, we need to find the set of values for \( u \) for which the function is defined.

Since this is a cube root function, we know that cube roots are defined for **all real numbers**. There are no restrictions on the domain from the cube root operation, unlike square roots which require non-negative numbers inside the radical.

Thus, the domain of \( h(u) \) is:

\[
\boxed{(-\infty, \infty)}
\]

### Would you like more details or have any further questions?

### Related Questions:
1. What is the range of the function \( h(u) = \sqrt[3]{u - 3} \)?
2. How would the domain change if this were a square root instead of a cube root?
3. How do you graph the function \( h(u) = \sqrt[3]{u - 3} \)?
4. What is the derivative of \( h(u) = \sqrt[3]{u - 3} \)?
5. How does shifting the function to \( h(u) = \sqrt[3]{u - 3} + 2 \) affect the domain?

**Tip:** For cube root functions, there are no domain restrictions, but always check for domain issues in even-root functions (like square roots).

State the domain of the function w = h(u) = ³√(u - 3)

Learn how to determine the domain of the cube root function h(u) = ³√(u - 3). This problem explores key algebraic concepts involving cube root functions and their domains. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation