Answer:
The domain of a square root equation is restricted to values of x that ensure the expression inside the square root is non-negative.
Explanation:
The domain of a function is the set of all possible input values (x-values).
For the square root function, f(x) = √x, the domain is restricted to values of x that ensure the expression inside the square root is non-negative. This restriction exists because in the real number system, we cannot take the square root of a negative number.
So, for the square root equation y =√x, the domain is expressed as:
- [0, ∞) in interval notation.
- x ≥ 0 in inequality notation.
This means that x can be any non-negative real number, including zero and all positive real numbers.
For other square root functions, such as f(x) = √(x - 2), the domain would be the values of x that makes the expression inside the square root non-negative, so x - 2 ≥ 0. Therefore, the domain of f(x) = √(x - 2) would be:
- [2, ∞) in interval notation.
- x ≥ 2 in inequality notation.