Chapter 10.1, Problem 3E

To determine

To describe the domain of square root function.

Answer to Problem 3E

Calculate the domain of a square root function, solve the inequality $x\ge 0$ with $x$ replaced by the radicand.

Explanation of Solution

Given information: Domain of a square root function

Calculation:

In mathematics, the domain of a function tells you for which values of $x$ the function is valid. This means that any value within that domain will work in the function, while any value that falls outside of the domain will not.

A square root function is a function that contains a radical, which is more commonly called a square root. If you aren't sure what this looks like, $f(x)=\sqrt{x}$ is considered a basic square root function. In this case, $x$ cannot be a positive number; all radicals must be equal to or greater than zero, or they produce an irrational number.

To calculate the domain of a square root function, solve the inequality $x\ge 0$ with $x$ replaced by the radicand. Using one of the examples above, you can find the domain of $f(x)=2\sqrt{\left(x+3\right)}$ by setting the radicand $\left(x+3\right)$ equal to $x$ in the inequality. This gives you the inequality of $x+3\ge 0$ , which you can solve by subtracting 3 by both sides. This gives you a solution of $x\ge -3$ , meaning that your domain is all values of x greater than or equal to -3. You can also write this as $[-3,\infty )$ , with the bracket on the left showing that -3 is a specific limit while the parenthesis on the right shows that 8 is not. Since the radicand cannot be negative, you only have to calculate for positive or zero values.