In mathematics, the domain and range of a function are the sets of input and output values, respectively, that are allowed and produced by the function.
The domain of a function is the set of all possible input values (usually represented by the variable x) for which the function is defined. It is the set of values that can be plugged into the function to produce a valid output. In other words, the domain is the set of all values of x that make the function meaningful and well-defined.
The range of a function is the set of all possible output values (usually represented by the variable y) that the function can produce for the given set of input values. In other words, it is the set of all values of y that the function can produce.
For example, consider the function f(x) = x^2. The domain of this function is all real numbers because any real number can be plugged into this function and produce a valid output. The range of this function is all non-negative real numbers, because the square of any real number is always non-negative.
It's important to note that the domain and range of a function may be affected by any restrictions or conditions placed on the function. For example, if a function involves a square root, the domain may be limited to non-negative values to ensure that the function is well-defined. Similarly, the range of a function may be restricted by the nature of the function itself.
