## HOW TO DETERMINE IF THE FUNCTION IS ONTO

How to determine if the function is onto ?

Here we are going to see how to determine if the function is onto.

Definition of onto function :

A function f : A -> B is said to be an onto function if every element in B has a pre-image in A. That is, a function f is onto if for each b  B, there is atleast one element a  A, such that f(a) = b.

This  is same as saying that B is the range of f . An onto function is also called a surjective function. In the above figure, f is an onto function

Let us look into some example problems to understand the above concepts.

Example 1 :

Check whether the following function is onto

f : N → N defined by f(n) = n + 2.

Solution :

Domain and co-domains are containing a set of all natural numbers.

If x = 1, then f(1)  =  1 + 2  =  3

If x = 2, then f(2)  =  2 + 2  =  4

From this we come to know that every elements of codomain except 1 and 2 are having pre image with.

In order to prove the given function as onto, we must satisfy the condition

Co-domain of the function  =  range

Since the given question does not satisfy the above condition, it is not onto.

Example 2 :

Check whether the following function is onto

f : R → R defined by f(n) = n2

Solution :

Domain  =  All real numbers

Co-domain  =  All real numbers

Since negative numbers and non perfect squares are not having preimage. It is not onto function.

Example 3 :

Check whether the following function are one-to-one

f : R - {0} → R defined by f(x) = 1/x

Solution :

Domain  =  all real numbers except 0

Co-domain  =  All real numbers including zero.

In co-domain all real numbers are having pre-image. But zero is not having preimage, it is not onto.

After having gone through the stuff given above, we hope that the students would have understood "How to determine if the function is onto".

Apart from the stuff given above, if you want to know more about "How to determine if the function is ontot", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6