To find the domain and range of the function f(x) = √x, we need to consider the restrictions on the input values (domain) and the output values (range).
1. **Domain**:
The domain of a square root function (√x) includes all the real numbers greater than or equal to zero since the square root of a negative number is not a real number. Therefore, for f(x) = √x, the domain is all real numbers x ≥ 0.
2. **Range**:
To determine the range, we consider the values that the function can output. The square root function always gives non-negative outputs because the square root of any non-negative number is a non-negative number. So, the range of f(x) = √x is all real numbers y ≥ 0.
In conclusion,
- Domain: x ≥ 0 (all non-negative real numbers)
- Range: y ≥ 0 (all non-negative real numbers)
