How to find the domain of a square root function?
Understand the Problem
The question is asking for the method to determine the domain of a square root function. The domain consists of all the input values (x) for which the function is defined, particularly where the expression inside the square root is non-negative.
Answer
(1) Identify the expression inside the square root, (2) Set it $\\geq$ 0, (3) Solve, (4) Write domain in interval notation. Example: $f(x) = \\sqrt{x-3}$ domain is $[3, \\infty)$
Answer for screen readers
To find the domain of a square root function, follow these steps: (1) Identify the expression inside the square root, (2) Set this expression to be greater than or equal to zero, (3) Solve the resulting inequality, and (4) Express the domain in interval notation. For example, for $f(x) = \sqrt{x-3}$, the domain is $[3, \infty)$
Steps to Solve
- Identify the expression inside the square root
First, find the mathematical expression that is inside the square root function. For example, if your function is $f(x) = \sqrt{x-3}$, the expression inside the square root is $x - 3$.
- Set the expression inside the square root to be non-negative
For a square root function to be defined, the expression inside the square root must be greater than or equal to zero. Set up an inequality to represent this condition. Using our example, we set $x - 3 \geq 0$.
- Solve the inequality
Solve the inequality obtained in the previous step to find the values of $x$ for which the inequality holds. For the example, solving $x - 3 \geq 0$ yields $x \geq 3$.
- Write the domain in interval notation
The solution to the inequality in step 3 gives us the domain of the function. In our example, the domain is $x \geq 3$, which can be written in interval notation as $[3, \infty)$.
To find the domain of a square root function, follow these steps: (1) Identify the expression inside the square root, (2) Set this expression to be greater than or equal to zero, (3) Solve the resulting inequality, and (4) Express the domain in interval notation. For example, for $f(x) = \sqrt{x-3}$, the domain is $[3, \infty)$
More Information
A fun fact: The concept of square roots dates back to ancient civilizations, with the Babylonians having a method for estimating square roots as early as 1900 BCE!
Tips
A common mistake is to forget that the expression inside the square root must be non-negative, leading to an incorrect domain. Always ensure you set up the inequality correctly and solve it accurately.
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