Question

How do you find the domain of $\sqrt{x+5}$ ?

Answer 1

To find the domain of the given function in x i.e. $\sqrt{x+5}$. We have to find the value of x where this function in the square root holds true. The function $\sqrt{x+5}$ exists when $x+5$ is always greater than and equal to 0. Because we know that the expression or number inside the square root must be greater than or equal to 0. So, apply this condition of the square root and find the value of x.

Complete step by step answer:
The function given in the above problem of which we have to find the domain is:
$\sqrt{x+5}$
We know that the number or expression inside the square root is always greater than and equal to 0 so as you can see that the expression written inside the square root is $x+5$. Hence, we are applying a condition in which $x+5$ is greater than and equal to 0.
$x+5\ge 0$
Subtracting 5 on both the sides we get,
$\begin{aligned} & x+5-5\ge 0-5 \\\ & \Rightarrow x\ge -5 \\\ \end{aligned}$
From the above calculations, we have found the range of x where the above function exists is equal to:
$x\ge -5$
Hence, we have calculated the domain of the above function as $x\ge -5$.

Note: To solve the above problem, we should know what a domain is and how to find the domain of any function. Also, having this knowledge of a domain is not sufficient. You should know that when the square root of a number or expression exists. If you don’t know how the square root will exist you cannot move further in this problem so make sure you know this information.