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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 :

GinnyAnsweridn
To determine the domain of the function [tex]\( y = \sqrt[3]{x} \)[/tex], we need to understand the behavior and limitations of a cube root function.

1. Understanding the Cube Root Function:
- The cube root function, [tex]\( \sqrt[3]{x} \)[/tex], 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.

2. Defining the Domain:
- Since the cube root of any real number exists and is a real number, there are no restrictions on the values of [tex]\( x \)[/tex]. In other words, [tex]\( x \)[/tex] can take any real value.

3. Expressing the Domain:
- The domain of [tex]\( y = \sqrt[3]{x} \)[/tex] is all real numbers, which can be written as [tex]\( -\infty < x < \infty \)[/tex].

Therefore, the correct choice for the domain of the function [tex]\( y = \sqrt[3]{x} \)[/tex] is:
[tex]\[ -\infty < x < \infty \][/tex]
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