# Function

## What is Composition of Functions ?

Here you will learn what is composition of functions with properties and examples. Let’s begin – What is Composition of Functions ? Let f : A $$\rightarrow$$ B & g : f : B $$\rightarrow$$ C be two functions. Then the function gof : f : A $$\rightarrow$$ C defined by (gof)(x) = g(f(x)) $$\forall$$ …

## Into Function – Definition and Examples

Here you will learn what is into function with definition and examples. Let’s begin – Into Function Definition Definition : A function f : A $$\rightarrow$$ B is said to be an into function if every element of B having no pre-image in A. In other words, f : A $$\rightarrow$$ B is an into …

## Onto Function (Surjection) -Definition and Examples

Here you will learn what is onto function with definition and examples. Let’s begin – Onto Function (Surjection) Definition Definition : A function f : A $$\rightarrow$$ B is said to be an onto function if every element of B is the f-image of some element of A i.e. , if f(A) = B or …

## Many One Function – Definition and Examples

Here you will learn what is many one function with definition and examples. Let’s begin – Many One Function Definition : A function f : A $$\rightarrow$$ B is said to be a many-one function if two or more elements of set A have the same image in B. Thus, f : A $$\rightarrow$$ B …

## One One Function (Injection) – Definition and Examples

Here you will learn what is one one function with definition and examples. Let’s begin – One One Function Definition Definition : A function f : A $$\rightarrow$$ B is said to be a one-one function or an injection if different elements of A have different images in B. Thus, f : A $$\rightarrow$$ B …

## Implicit and Explicit Function – Definition and Example

Here you will learn what is implicit and explicit function with definition and examples. Let’s begin – Implicit and Explicit Function Definition : A function defined by an equation not solved for the dependent variable is called implicit function. e.g. the equations $$x^3 + y^3$$ = 1 and $$x^y$$ = $$y^x$$, defines y as an …

## Cube Function – Graph, Definition, Domain and Range

Here you will learn what is cube function with definition, graph, domain and range. Let’s begin – Cube Function Definition and Formula The function that associates a real number x to its cube i.e. $$x^3$$ is called the cube function. Since $$x^3$$ is defined for all x $$\in$$ R. So, we defined the cube function …

## Square Function – Graph, Definition, Domain and Range

Here you will learn what is square function with definition, graph, domain and range. Let’s begin – Square Function The function that associates a real number x to its square i.e. $$x^2$$ is called square function. Since $$x^2$$ is defined for all x $$\in$$ R. So, we defined the square function as follows : Definition …