Question

Find the domain of the function. $$y=6 \sqrt{x}$$

Short answer

The domain of the function \(y=6 \sqrt{x}\) is \(x \geq 0\) (all real numbers that are greater than or equal to zero).

Step-by-step solution

Understand the Function

The function given is \(y = 6 \sqrt{x}\) where \(y\) is dependent on the value of \(x\). The value underneath the square root function (\(x\)) must be greater than or equal to zero. This is because square root of a negative number isn't defined in the real number system.

Determine the Domain

From the understanding developed in step 1, one knows that \(x\) must be either zero or a positive real number for the given function to be defined in real numbers. Hence, the domain is all real numbers that are greater than or equal to zero.