$20 Bonus + 25% OFF
Securing Higher Grades Costing Your Pocket? Book Your Assignment at The Lowest Price Now!
Add File

Error goes here

Define The One To One Function With Examples

Referencing Styles : APA | Pages : 1

In mathematics, the function can be defined as an expression or rule that defines the relationship between the variables. There is mainly two kinds of variables that is dependent and independent one. Function is defined to be ubiquitous in mathematics and is very much important for the formulation of relationship in science. In the year 1837, the latest definition of function was given by Peter Dirichlet. The given relationship is commonly symbolized as y=f(x). Also, another abbreviated symbol that is g(x) and P(x) is mainly used for representing the function of independent of variable x.  It is mainly done in some specific condition which is completely unknown or unspecified. In other words, a function can be defined as a relationship where the quantity that is dependent variable completely depends or is determined by the help of another quantity that is an independent variable. It can be said that the dependent variable as a function of an independent variable.

Some of the commonly used mathematical formulas are defined as the known function. The formula for the circle of the area is given by A = πr2. In this, dependent variable A is considered to be a function of an independent variable which is of various r. The function requires involvement of two or more variables which are considered to be common in mathematics. In the formula of area of a triangle, A= ½ (based * Height). In the given example, a physical constraint that is force is the independent variable which is found to be a positive number. There are many instances when the independent variable is allowed to have negative values which are any real number. Then it is known to be a real-valued function.

The formula of area of a circle is given by a polynomial function. The general form of the given function is

P(x) = a0a1x + a2x2+anxn,

Where all the co-efficient that is (a0a1a2,…, an) is provided. All the counting power of x are nothing but the counting number (1,2,3….). Polynomial function has completely studied in the beginning times because of versatility which requires the involvement of real numbers. It can be closely approximated by the help of polynomial function. There are many polynomial functions is completely characterized by the highest for an independent variable. Some of special names that are known common are the powers of one to five that is linear to quantic.

A polynomial function can be provided by a geometrical representation which is done by the help of analytical geometry. The independent variable X is plotted along the X-axis (horizontal line) and the dependent variable y is put on the y-axis (vertical line). Graph function comes up with two co-ordinates (x, y) where y = f(x). Another kind of function which has been studied right from the antiquity are a trigonometric function that is Sin X and Cos X, which is defined as the measure of an angle. As a result of periodic nature, trigonometric functions are mainly used like a model which repeats or cycles. Trigonometric functions are a non-algebraic function which is also known as a transcendental function.

The only practical application of the given function is the variable which is defined as a complex number which is not that much easy to explain. It is nevertheless very much extensive. It mainly used in various domains like electrical engineering and aerodynamics. A complex variable is mainly represented in the form z=X+iY where i is defined as an imaginary number. The value of i is equal to the square root of -1 which have two variables x and y considered as real variables. The possible method of splitting the complex function is in between two parts that are real and imaginary.

An individual can have an inverse function by interchanging the roles of independent and dependent variables for a given function. Inverse function performs as per the name where they need to undo action of function so that they ca return variable to original state. For a given f(x) there exist a function g(y) in such a way g(f(x)) = x and f(g(y))=y then g is defined as the inverse function of the given function f and denoted by f-1 . Hereby convention the variables are completely interchanged. For given example, the function f(x)= 2x comes up with inverse function f-1(x) = x/2.

A given function f: A → B can be stated as one to one function if f (a1) = f (a2 )

Where (a1 )= (a2 ), (a1 ) (a2 )  A

Let us consider A = {(a 1 )( a 2 )( a 3 )( a 4 )} and B = {( b 1 )( b 2 )( b 3 )( b 4 )}


Fig 1: One to One Function

For example: The given function provided below can be taken to be one to one.

1. Each state of India assigns its capital city.

Ans: This is not a one to one function as each state of India comes up with different capital.

2. Function f = {(2,4), (3,6), (-1, -7)}

Ans: This function is one to one just because of one to one as each of the value range comes up with a different value of domain.

3. F(x) = |x|

Ans: In this function, we need to check whether the given function is one to one or not. Now, some of the core values of x (domain) and given function we need to find the value of range.












From the above table the point can be noted that the value in the given range repeats so it is not considered to be one to one function.


Fig 2: Three Graphs for Determining One to One function

In the 1st graph, if horizontal line is drawn then the line cuts the graph at the given point only one point. So the 1st graph can be stated as one to one graph function.

In the 2nd graph, if a horizontal line is drawn then the line cut the graph at any two point so second graph at point is 1 to 1 graph function.

In the 3rd graph,  if a horizontal line is drawn then the given line cuts the graph into two given point so it non a one to one function.


OR is the best assignment help provider serving thousands of students in New York City, Boston, Washington D.C. and Chicago. With a team of qualified and experienced online assignment experts, we deal with all types of assignment writing tasks. Our popular assignment help services include marketing assignment help, auditing assignment help, finance assignment help, statistics assignment help, help with law assignments. We guarantee that students, who decide to buy assignments online, get work worth their money and time.

Save Time & improve Grade

Just share requirement and get customized Solution.

We will use e-mail only for:

arrow Communication regarding your orders

arrow To send you invoices, and other billing info

arrow To provide you with information of offers and other benefits

Add File

Error goes here




Overall Rating



Our Amazing Features


On Time Delivery

Our writers make sure that all orders are submitted, prior to the deadline.


Plagiarism Free Work

Using reliable plagiarism detection software, only provide customized 100 percent original papers.


24 X 7 Live Help

Feel free to contact our assignment writing services any time via phone, email or live chat. If you are unable to calculate word count online, ask our customer executives.


Services For All Subjects

Our writers can provide you professional writing assistance on any subject at any level.


Best Price Guarantee

Our best price guarantee ensures that the features we offer cannot be matched by any of the competitors.

Our Experts

Assignment writing guide
student rating student rating student rating student rating student rating 5/5

2830 Order Completed

97% Response Time

Leroy Bicknell

MBA in Marketing

London, United Kingdom

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 5/5

755 Order Completed

95% Response Time

Douglas Cowley

Masters in Finance with Specialization in Audit

Wellington, New Zealand

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 4/5

248 Order Completed

100% Response Time

Lloyd Bernabe

MSc in Accounting

London, United Kingdom

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 5/5

647 Order Completed

98% Response Time

Adlina Han

Masters in Marketing with Specialization in Branding

Singapore, Singapore

Hire Me

FREE Tools


Plagiarism Checker

Get all your documents checked for plagiarism or duplicacy with us.


Essay Typer

Get different kinds of essays typed in minutes with clicks.


GPA Calculator

Calculate your semester grades and cumulative GPa with our GPA Calculator.


Chemical Equation Balancer

Balance any chemical equation in minutes just by entering the formula.


Word Counter & Page Calculator

Calculate the number of words and number of pages of all your academic documents.

Refer Just 5 Friends to Earn More than $2000

Check your estimated earning as per your ability




Your Approx Earning

Live Review

Our Mission Client Satisfaction

Will use again, sometimes I have issues getting the creative part of writing going and love being able to reach out to help with drafts


User Id: 436303 - 23 Jan 2021


student rating student rating student rating student rating student rating

The best way to paraphrase is to change every few words in the sentence or paragraph I want to use in my assignment.


User Id: 160343 - 23 Jan 2021


student rating student rating student rating student rating student rating

good and excellent I am satisfied with your work. All the work done on time. Experts are good.


User Id: 160343 - 23 Jan 2021


student rating student rating student rating student rating student rating

One of the best service in the Market. The assignment was completed in time, and I\'ve got a perfect rewrite option as well. The IT Support helped me to deal with all the technical issues. The Sales Department was polite and attentive. Definitely sho...


User Id: 577967 - 23 Jan 2021


student rating student rating student rating student rating student rating
Define The One To One Function... has been added in your library.
callback request mobile
Have any Query?