Question

Find the domain of the function. $$y=0.2 \sqrt{x}$$

Short answer

The domain of the function \(y=0.2 \sqrt{x}\) is \([0, \infty)\).

Step-by-step solution

Understanding the Square Root Function

The primary rule to consider while defining the domain of a square root function is that the term under the square root cannot be negative. This is due to the property of real numbers that square root of a negative number is undefined.

Define the Domain

The function is \(y=0.2 \sqrt{x}\). The term under the square root is 'x'. Since it can't be negative, this implies that \(x\) must be greater than or equal to 0. Thus, the domain of the function are all real numbers that are greater than or equal to zero, often written as \([0, \infty)\).