Understanding the Range of a Function: Exploring the Set of Possible Outputs in Mathematics

Range (aka Codomain)

In mathematics, the range, also known as the codomain, refers to the set of all possible values that a function can output

In mathematics, the range, also known as the codomain, refers to the set of all possible values that a function can output. It is the set of all possible results or outputs of the function.

To understand the range of a function, let’s consider a simple example. Suppose we have a function f(x) = x^2. This function takes any real number x as input and squares it to give an output.

To find the range of this function, we need to determine all the possible values that the function can output. Since we are squaring the input, the result will always be a non-negative number (i.e., greater than or equal to 0). Thus, the range of this function is [0, ∞) which denotes all real numbers from 0 to positive infinity.

In some cases, functions may have restrictions on their domains, which can impact the range. For example, consider the function g(x) = 1/x. Here, the domain of this function excludes the value x = 0, as division by zero is undefined. In this case, the range of the function would be all real numbers except for 0.

It is important to note that range can be limited by the nature of the function, its domain, or any constraints imposed by the problem. In other cases, the range may be the entire set of real numbers or a specific subset of them, depending on the function.

To summarize, the range (or codomain) of a function is the set of all possible values that the function can produce as output. It can be determined by analyzing the nature of the function, its domain, and any additional restrictions or constraints.

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