We are familiar with Domain of a Function and Range of a Function. But what does it mean? before diving deeper in to the topic, let us understand what is a function?
Functions are one of the very important concepts in mathematics which has got numerous applications in real world. Be it the mega skyscrapers or super-fast cars, their modeling requires methodical application of functions. Almost all the real world problems are formulated interpreted and solved using functions.
An understanding of relations is required in order to understand functions. And understanding of Cartesian products is required to understand relations. A Cartesian product of two sets \(A\)
Definition 1: A relation \(F\)
To understand the difference between relations and functions, let us take an example. Set \(A\)
But if we define a relation \(F\)
Domain and Range of a Function:
Remember that in case of a relation, the domain might not be same as the left set in the arrow diagram. This is because the set may contain any element which doesn’t have an image in the right set. But in case of functions, domain will always be equal to the first set. Range and Codomain of a function are defined in the same way as they are defined for relations. Let us look at some definitions with examples to understand better.
Definition 2: The set of all possible values which qualify as inputs to a function, is known as the domain of the function.
For e.g. the domain of the function \(F\)
Definition 3: The set of all the outputs of a function is known as the range of the function \(x \)
For e.g. the range of the function \(F\)
Till now, we have represented functions with upper case letters but they are generally represented by lower case letters. If \(f\)
There are several types of functions and some of them even have got funny names e.g. floor function, ceiling function, etc. To know more, visit www.byjus.com and experience fun in learning.