A function in mathematics is defined within a specified range, and we define domain terms for that. However, this topic is not only limited to this aspect. It would help if you dive in to understand it in a better way. First, you need to understand the proper definition for a function, its domain, range and codomain. Considering the simplest form of a function, it is defined as the values that can satisfy a function's conditions. The range is defined as the output that we get after solving a function.
The domain can be defined as the set which is the input of the function. Or in simple terms, it is the input values that are used for a function. A function’s values can be defined as the values that are defined on a set.
The range can be defined as the actual output which we are supposed to get after we enter the function’s domain. The range is dependent on the variables of the functions. The codomain can be defined as the total number of values present in a set. They are thus the values which are expected to come out when the domain values are entered. The set of all the possible values which qualifies the inputs of a function is called the domain or it can be defined as the entire set of values which is possible for variables that are independent. The domain can be found in the fraction’s denominator which is not equal to zero and the digit present under the square root bracket.
How will you Define a Function for a Domain Range?
A function is a way to relate input to get its output. In real-time, functions are the necessary part of understanding and implementing. Also, functions are required for methodical applications. Thus, you can solve different real-world problems with it.
If you want to understand a function and relation between two functions, this is possible with a cartesian product. The basic points to define a function includes:
A function will relate each value of one set to the values of another set. It can be the same set or a different one. A set is the collection of values, numbers or things.
Consider the below diagram:
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In the above diagram, X and Y are two sets and function is defined from values of X to that of Y.
Domain and Range of a Function
Not all the values are specified for a function. Some specifications define it as what can be put into a function to get the desired results. There are three terms that are to be defined for a function:
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According to the diagram, Domain is the entire set A and codomain is set as the whole B, and Range is the outcome after entering domain values. Or simply saying, the range is the pointed values of set B.
How to Relate Codomain and Range?
In short terms, we can say that range is the subset of the codomain. It is not important that a function might satisfy all the values of the codomain. However, the values that we get after entering domain values in a function are the range. Thus, it is part of the codomain set.
Difference Between Codomain and Range
Without a doubt, both codomain and range are present on the output side. However, there is a difference between the two of them. Codomain is defined as the possibility of the values as an outcome. Thus we can say that codomain is one part while defining a function. However, on the other hand, the range is the actual output that we are supposed to get.