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… Continue reading Graph of An Inverse Function
Category: Calculus
Steps To Find An Inverse Function
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 =… Continue reading Steps To Find An Inverse Function
Surjective Function
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… Continue reading Surjective Function
Onto Function
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… Continue reading Onto Function
What Is Inverse Function?
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… Continue reading What Is Inverse Function?
Inverse Function
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… Continue reading Inverse Function
Identification of a Function in Math
A function in math means a correspondence from one value x of the first set to another value y of the second set. This correspondence can be of the following four types. But every correspondence is not a function. In the example below, only 1 – 1 and many to one are examples of a function because… Continue reading Identification of a Function in Math
Representation of Functions in Math
The rule which specifies a function can come in many different forms based on how it is defined. They can be defined as piecewise-defined-functions or as formulas. When we define f(x) = √x, for x ≥ 0, then the inputs are the numbers that we provide and the ‘taking square root’ function accepts all non-negative real numbers… Continue reading Representation of Functions in Math
Functions in Math
Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such… Continue reading Functions in Math
Precalculus
Precalculus in mathematics is a course that includes trigonometry and algebra designed to prepare students for the study of calculus. In precalculus, we focus on the study of advanced mathematical concepts including functions and quantitative reasoning. Some important topics covered under precalculus are, Functions Inverse Functions Complex Numbers Rational Function