In mathematics, the domain and range are two related but distinct concepts that describe the input and output values of a function, respectively.
The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of values that can be plugged into the function to produce a valid output. For example, if we consider the function f(x) = sqrt(x), the domain of this function is all non-negative real numbers (i.e., x >= 0), because the square root of a negative number is not a real number.
The range of a function, on the other hand, is the set of all possible output values that the function can produce. In other words, it is the set of values that the function can take on as its output. For example, if we consider the function f(x) = x^2, the range of this function is all non-negative real numbers (i.e., y >= 0), because a square of a real number is always non-negative.
In summary, the domain and range of a function are both important concepts that describe the input and output values of the function, respectively. The domain is the set of all possible input values for which the function is defined, while the range is the set of all possible output values that the function can produce. Understanding these concepts is important in analyzing and graphing functions, as well as in solving problems involving functions.
