Fill in the blank(s) to correctly complete each sentence. The function g(x)=√x has domain ________.

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1. <The function \( g(x) = \sqrt{x} \) is defined for all values of \( x \) where the expression under the square root is non-negative.>
2. <This means that \( x \) must be greater than or equal to zero, as the square root of a negative number is not defined in the set of real numbers.>
3. <Therefore, the domain of \( g(x) = \sqrt{x} \) is all real numbers \( x \) such that \( x \geq 0 \).>
4. <In interval notation, this domain is expressed as \([0, \infty)\).>
5. <This means that the function \( g(x) = \sqrt{x} \) can take any non-negative real number as input.>

Key Concepts

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For the function g(x) = √x, the domain is restricted to non-negative values because the square root of a negative number is not a real number. Thus, understanding the domain is crucial for determining valid inputs.

Square Root Function

The square root function, denoted as √x, is a mathematical function that returns the non-negative value whose square is x. This function is only defined for non-negative inputs, meaning that for any x < 0, g(x) is undefined. Recognizing the properties of the square root function helps in identifying its domain.

Real Numbers

Real numbers include all the numbers on the number line, encompassing both rational and irrational numbers. In the context of the function g(x) = √x, it is important to note that the function only accepts real numbers as inputs. Therefore, understanding the distinction between real and non-real numbers is essential for determining the function's domain.