What is a Function

What is a Function in Maths?

A function in mathematics is a relation between the input values (domain) and the output values (range) of the given sets such that no two variables from the domain sets are linked to the same variable in the range set. A simple example of a function in math is f(x) = 2x, which is defined on R→R, here any variable in the domain is related to only one variable in the range....

Functions Examples

A function in mathematics f is defined as, y = f(x) where x is the input value, and for each input value of x, we get a unique value of y. Various examples of the functions in math defined on R→R are,...

Condition for a Function

For any two non-empty sets A and B, a function f: A→B denotes that f is a function from A to B, where A is a domain and B is a co-domain....

Representation of Functions in Math

We represent a function in mathematics as,...

Identification of Function

Function is classified as a special type of relation in math. There are following rules which can be used to identify a function:...

Types of Function

Different Types of Functions are used to solve various types of mathematical problems especially related to curves and equations. There are three major types functions in mathematics that are based on the element mapping from set A to set B....

What is a Function in Algebra?

A function in algebra is an equation for which any x that can be put into the equation will produce exactly one output such as y out of the equation. It is represented as y = f(x), where x is an independent variable and y is a dependent variable....

Composition of Functions

If f: A → B and g: B→ C be two functions. Then the composition of f and g is denoted as f(g) and it is defined as the function fog = f(g(x)) for x ∈ A....

Algebra of Functions

Algebra of Functions involve the algebraic operations performed between two functions. The algebraic operation for two functions f(x) and g(x) defined on the real value of x are mentioned below:...

What is a Function on a Graph?

A function can be easily represented on a graph. Any function on graph represent a curve (including straight line) in the x-y plane mapped for its input and corresponding output values....

Common Functions

Some Common Function that commonly used in mathematics are discussed below:...

Applications of Functions

When we say that a variable quantity y is a function of a variable quantity x, we indicate that y is dependent on x and that y’s value is determined by x’s value. This dependency can be expressed as follows: f = y (x)....

Examples on Function

Example 1: For two functions f and g are defined as, f(x) = x2 and g(x) = ln(2x). Find the composite function (gof )( x )...

Practice Problems on What is a Function

1. Given the function f(x)=3x+5...

Summary – What is a Function

A function in mathematics is a special relation between input values (domain) and output values (range) where each input is associated with a unique output. Represented as y = f(x), functions have specific characteristics and can be visualized using ordered pairs, tables, or graphs. They are essential in various mathematical problems and come in different types, including injective (one-to-one), surjective (onto), and bijective (both). Functions can be tested using the vertical line test and are classified further into polynomial, inverse, exponential, logarithmic, and trigonometric functions. Understanding functions involves recognizing their domain, range, and the rules defining them. Examples include simple linear functions like y = 2x + 1 and complex compositions of functions. Functions play a crucial role in algebra, geometry, and calculus, aiding in the representation and analysis of mathematical relationships and real-world phenomena....

FAQs on What is a Function

What is the definition of a function?...