The domain for function f(x) = cubed root of x  is [0, positive infinity). is this true ?

No, the domain of the function \( f(x) = \sqrt[3]{x} \) is not restricted to \([0, \infty)\). This statement is false.

The cube root function \( \sqrt[3]{x} \) is defined for all real numbers because any real number, whether positive, negative, or zero, has a real cube root. Therefore, the correct domain of \( f(x) = \sqrt[3]{x} \) is:

\[
\text{Domain} = (-\infty, \infty)
\]

Unlike square roots, cube roots can handle negative inputs because the cube of a negative number is also negative. For example, \( \sqrt[3]{-8} = -2 \).

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the domain of \( f(x) = \sqrt[4]{x} \)?
2. What is the range of \( f(x) = \sqrt[3]{x} \)?
3. How do cube root and square root functions differ in terms of their domains?
4. Can the cube root function be expressed as a power function?
5. What is the inverse function of \( f(x) = \sqrt[3]{x} \)?

**Tip:** When determining the domain of a function, check whether there are any restrictions on the input values, such as square roots or logarithms, which only allow non-negative values.

The domain for function f(x) = cubed root of x is [0, positive infinity). Is this true?

Understand why the domain of the cube root function f(x) = √[3]{x} is not limited to [0, ∞) but rather spans all real numbers. This explanation explores key mathematical concepts, including cube roots and the domain of functions, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation