Answer:
No real square root of a negative
Step-by-step explanation:
It all comes down the the square root of x. There is no real square root of a negative number so x must be equal to or greater than 0.
Domain is therefore x >= 0.
The domain in most contexts refers to the independent variable---what you can choose to put in the function.
The answer comes from realizing that square roots real numbers are only defined for non-negative numbers. For example, √(4) = 2 and it represents the number such that multiplying it by itself will get 4, i.e. √(4) · √(4) = 2 · 2 = 4.
But positive times a positive makes a positive product, and negative times a negative also results in a positive product. It is not possible to find a real number such that multiplying it by itself gives you a negative number. The two real numbers being multiplied together must have the same sign because those two numbers are the same number.
This tells us that for 3√(x), we must have that whatever is inside the square root is nonnegative. Hence the domain of the function is x ≥ 0. (Square root of 0 is 0.)
