Category: Inverse Functions

The injective function is the reflection of the origin function with reference to the line y = x, and is obtained by swapping (x, y) with the (y, x). If the graphs of two functions are given, we can identify whether they are inverses of each other. If the graphs of both functions are symmetric…

The following sequence of steps would help in conveniently finding the inverse of a function. Here we consider a function f(x) = ax + b, and aim at finding the inverse of this function through the following steps. For the given function f(x) = ax + b, replace f(x) = y, to obtain y =…

A surjective function is defined between set A and set B, such that every element of set B is associated with at least one element of set A. The domain and range of a surjective function are equal. Let us learn more about the surjective function, along with its properties and examples. What Is a Surjective Function? Surjective…

Onto function is a function f that maps an element x to every element y. That means, for every y, there is an x such that f(x) = y. Onto Function is also called surjective function. The concept of onto function is very important while determining the inverse of a function. In order to determine if a…

The inverse of a function f is denoted by f-1 and it exists only when f is both one-one and onto function. Note that f-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x. (f o f-1) (x) = (f-1 o f) (x) = x…

Inverse function is represented by f-1 with regards to the original function f and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with…