Question

How do I find the domain of the square root function?

Answer 1

Hint: In this problem, we have to find the domain of square root function. We can take any one of the examples for square root function to find its domain. We can first set the expression inside the square root greater than or equal to zero, we can take this because only non-negative numbers have real square roots. We should know that while writing an inequality to find the domain, if we multiply or divide a number by a negative number, then we have to reverse the inequality symbol.

Complete step by step answer:
We have to find the domain of the square root function.
We can take an example to solve this problem.
We can first set the expression inside the square root greater than or equal to zero, we get
We set the expression x+3 inside the square root,
\[\Rightarrow f\left( x \right)=\sqrt{x+3}\]
Now the above expression x+3 inside the square can only be greater than or equal to 0, for real numbers.
\[\begin{align}
  & \Rightarrow x+3\ge 0 \\
 & \Rightarrow x\ge -3 \\
\end{align}\]
We have found the value of x, we can write it in interval notation, we get
\[\left[ -3,\infty \right)\]
Therefore, the domain of the square root expression \[f\left( x \right)=\sqrt{x+3}\] is \[\left[ -3,\infty \right)\].

Note:
Students make mistakes while multiplying or dividing the inequalities, we should know that while writing an inequality to find the domain, if we multiply or divide a number by a negative number, then we have to reverse the inequality symbol. We should also know that if the number inside the square root is not greater than or equal to 0, then it gives an imaginary value.