**Bijective function :**

Let f : A ----> B be a function.

The function f is called an one-one and onto or a bijective function if f is both a one-one and an onto function

More clearly,

f maps distinct elements of A into distinct images in B and every element in B is an image of some element in A.

The figure given below represents a one to one and onto or bijective function.

Apart from the bijective function, we have some other functions on sets.

**Let us discuss the other different types of functions here:**

The other different types of functions on sets are

(i) One to one or Injective function

(ii) Onto or Surjective function

(iii) Constant function

(iv) Identity function

Let us discuss the above different types of functions in detail.

Let f : A ----> B be a function.

The function f is called an one-one function, if it takes different elements of A into different elements of B.

That is, we say f is one-one

In other words f is one-one if no element in B is associated with more than one element in A.

A one-one function is also called an Injective function.

The figure given below represents a one-one function.

Let f : A ----> B be a function.

The function f is called an onto function, if every element in B has a pre-image in A.

That is, in B all the elements will be involved in mapping.

An onto function is also called a surjective function.

The figure given below represents a onto function.

The function f is called constant function if every element of A has the same image in B.

Range of a constant function is a singleton set.

Let A = { x, y, u, v, 1 }, B = { 3, 5, 7, 8, 10, 15 }.

The function f : A ---> B defined by f (x) = 5 for every x belonging to A is a constant function.

The figure given below represents a constant function.

Let A be a non-empty set. A function f : A ---> A is called an identity function of A if f (a) = a for all a belonging to A.

That is, an identity function maps each element of A into itself.

For example, let A be the set of real numbers (R). The function f : R ----> R be defined by f (x) = x for all x belonging to R is the identity function on R.

The figure given below represents the graph of the identity function on R.

Let f : A ----> B be a function.

Then, we have

**Domain : Set A**

**Co-domain : Set B**

**Range : Elements of B involved in mapping. **

Note :

In onto function, co-domain = Range

After having gone through the stuff given above, we hope that the students would have understood "Bijective function".

Apart from the stuff given above, if you want to know more about "Bijective-function", please click here

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**