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

Integration, Integration of square root of sin

Integration of square root of sin

Matrix, matrix of [1 4 ] [a b]=4/9

matrix of [1 4 ] [a b]=4/9

Square of a number added to 25 equals 10 times the number, The square of a ...

The square of a number added to 25 equals 10 times the number. What is the number? Let x = the number.  The statement, "The square of a number added to 25 equals 10 times the n

Puzzle, 0+50x1-60-60x0+10

0+50x1-60-60x0+10

Number sequence, what is the formula to find a sequence on a string of numb...

what is the formula to find a sequence on a string of numbers?

1, use 3/8 of a thin of paint, what fraction of the paint is left in thin (...

use 3/8 of a thin of paint, what fraction of the paint is left in thin (show work

Ratios, 450 students. if there are 50 more boys than girls, how many boys a...

450 students. if there are 50 more boys than girls, how many boys and girls are there?

Example for comparison test for improper integrals, Example for Comparison ...

Example for Comparison Test for Improper Integrals Example:  Find out if the following integral is convergent or divergent. ∫ ∞ 2 (cos 2 x) / x 2 (dx) Solution

Measurement story problem, Seth has a pet goldfish. When he got his goldfis...

Seth has a pet goldfish. When he got his goldfish , it was only 5 centimeters long . Now it has grown to be 92 millimeters long. How many millimeters has the goldfish grown since

Graphical method for interpolation, Graphical Method Whil...

Graphical Method While drawing the graph on a natural scale, the independent variables are marked along the horizontal line and corresponding dependen

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