What is the domain of the function [tex]y=\sqrt{x}[/tex]?
A. [tex]-\inftyB. [tex]0C. [tex]0 \leq x<\inftyD. [tex]1 \leq x<\infty
Answer (2)
The function is y = x .
The domain of the function is the set of all possible values of x for which the function is defined.
The square root function is only defined for non-negative values.
Therefore, x must be greater than or equal to 0, which can be written as 0 ≤ x < ∞ .
The domain of the function y = x is 0 ≤ x < ∞ .
Explanation
Understanding the Problem We are asked to find the domain of the function y = x . The domain of a function is the set of all possible values of x for which the function is defined.
Square Root Function The square root function, denoted as x , is only defined for non-negative values of x . This means that the value inside the square root must be greater than or equal to 0.
Inequality Condition Therefore, we must have x ≥ 0 . This inequality represents all non-negative real numbers.
Interval Notation In interval notation, the domain of the function y = x is [ 0 , ∞ ) . This means that x can be any real number greater than or equal to 0.
Final Answer The correct answer is 0 ≤ x < ∞ .
Examples
The domain of a square root function is a fundamental concept in mathematics and has practical applications in various fields. For example, in physics, when calculating the speed of an object using the formula v = m 2 K E , where K E is the kinetic energy and m is the mass, the kinetic energy must be non-negative to obtain a real value for the speed. Similarly, in engineering, when designing structures involving square root relationships, ensuring that the input values are within the domain is crucial for accurate and reliable results. Understanding the domain helps avoid undefined or imaginary results in real-world calculations.
The domain of the function y = x consists of all non-negative values of x . Therefore, it is expressed as 0 ≤ x < ∞ . The correct answer is option C: 0 ≤ x < ∞ .
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