One-to-one function, Mathematics

Assignment Help:

One-to-one function: A function is called one-to-one if not any two values of x produce the same y.  Mathematically specking, this is the same as saying,

 f ( x1 ) ≠ f ( x2 )

whenever  x1 ≠ x2

Thus, a function is one-to-one if whenever we plug distinct values into the function we get different function values. Sometimes it is simpler to understand this definition if we illustrates a function that isn't one-to-one.

 Let's take a look at a function which isn't one-to-one.  The function f ( x )= x2  is not one-to-one since both f ( -2) = 4 and f ( 2) = 4 .  In other terms there are two different values of x that generate the same value of y.  Note down that we can turn f ( x ) = x2  into a one-to-one function if we limit ourselves to 0 ≤ x <∞ .  It can sometimes be done with functions.

Illustrating that a function is one-to-one is frequently tedious and/or difficult.  For the most part we are going to suppose that the functions which we're going to be dealing with in this course are either one-to-one or we have limited the domain of the function to get it to be a one-to-one function.

Now, let's formally define just what inverse functions are.


Related Discussions:- One-to-one function

Can religious wars be avoided in the future, To what extent do you think re...

To what extent do you think religious beliefs should justify war? How is this shown in "The Song of Roland"? Cite examples of how religious beliefs have led to war in the last two

Transition matrix for the probabilitiy, Suppose research on three major cel...

Suppose research on three major cell phones companies revealed the following transition matrix for the probability that a person with one cell phone carrier switches to another.

What is the value of the largest consecutive integer, The sum of three cons...

The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer? Three consecutive even integers are numbers in order such as 4, 6, and

Solving trig equations with calculators, Solving Trig Equations with Calcul...

Solving Trig Equations with Calculators, Part I : The single problem along with the equations we solved out in there is that they pretty much all had solutions which came from a

What is partially ordered set, What is Partially Ordered Set?  Let  S = {a,...

What is Partially Ordered Set?  Let  S = {a,b,c} and A = P(S). Draw the Hasse diagram of the poset A with the partial order ⊆ (set inclusion).   Ans: Let R be a relation define

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd