Domain and range are very significant in a function. In mathematics, the domain of a function refers to the set of all input values (also referred to as the independent variables) that are allowed to plug into a function; for which the function is defined. The range of a function refers to the set of all output values (also referred to as the dependent variable) that the function generates.
Like, take the example of the function f (x) = x^2. The domain of this function is all real numbers as the function defines any real value of x. The range of this function is also all real numbers as the function can generate any real number as output when given inputs are real numbers.
Now, take the function g (x) = 1/x. This function cannot be considered for x = 0, as division by zero is not permitted. So, the domain of this function refers to all real numbers, excluding 0. The range of this function also refers to all real numbers, excluding 0, as the function can generate output as any nonzero real number when the given input is a nonzero real number.
It is necessary to observe that the domain and range of a function may be restricted by the structure of the function itself, and also by any limitations or checks on the variables. There is also a possibility of domain and range being infinite sets, like the set of all real numbers or the set of all positive integers.
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