Question

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

Short answer

The domain of the function \( y = x \sqrt{x} \) is \( x \geq 0 \), or in interval notation, \([0, +\infty)\)

Step-by-step solution

Identify the Function

First, let's look at the function: \( y = x \sqrt{x} \). Here, \( x \) is the variable we're interested in determining the domain for.

Determine the Limits for x

Looking at the function, we can see that \( x \) is under a square root. Therefore, \( x \) can't be a negative number because the square root of a negative number is not real. Therefore, \( x \) needs to be greater than or equal to 0. That is, \( x \geq 0 \). This is our domain.

Write the Domain

Finally, you write out the domain. In interval notation, the domain of the function would be written as \([0, +\infty)\), or in inequality notation, \( x \geq 0 \)