The domain and range of a function are both important concepts in mathematics that describe the input and output values of the 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.
Understanding the domain and range of a function is important because it helps us to identify the valid input and output values for the function, respectively. It can also help us to analyze and graph the function, and to solve problems involving the function.
In summary, the domain of a function is the set of all possible input values for which the function is defined, while the range of a function is the set of all possible output values that the function can produce.
