Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

What is the domain of the function [tex]y=\sqrt[3]{x}[/tex]?

A. [tex]-\infty \ \textless \ x \ \textless \ \infty[/tex]
B. [tex]0 \ \textless \ x \ \textless \ \infty[/tex]
C. [tex]0 \leq x \ \textless \ \infty[/tex]
D. [tex]1 \leq x \ \textless \ \infty[/tex]

Sagot :

GinnyAnswer
Let's analyze the function [tex]\( y = \sqrt[3]{x} \)[/tex] in order to determine its domain.

The cube root function [tex]\( \sqrt[3]{x} \)[/tex] is the inverse of the cube function [tex]\( x^3 \)[/tex]. An important property of the cube root function is that it is defined for all real numbers. This means that you can take the cube root of any real number, whether it is positive, negative, or zero.

For example:
- The cube root of a positive number [tex]\( \sqrt[3]{8} = 2 \)[/tex].
- The cube root of zero [tex]\( \sqrt[3]{0} = 0 \)[/tex].
- The cube root of a negative number [tex]\( \sqrt[3]{-8} = -2 \)[/tex].

Since there are no restrictions on the values that [tex]\( x \)[/tex] can take for the function [tex]\( y = \sqrt[3]{x} \)[/tex], the domain includes all real numbers.

Thus, the domain of the function [tex]\( y = \sqrt[3]{x} \)[/tex] is:

[tex]\[ -\infty < x < \infty \][/tex]

Therefore, the correct answer is:
[tex]\[ -\infty < x < \infty \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.