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

Find out the mean time, 1 . The probability that a couple will have a child...

1 . The probability that a couple will have a child with black hair is 0.6. If this couple has 7 children what is (a) the probability that exactly 3 of these children have bl

Example of the invisible effort, Imagine a time in history when the number ...

Imagine a time in history when the number system had not yet evolved a farmer needed to keep track of his cattle. What would he do to figure out whether his entire rattle returned

Immediate predecessor of mahavira, The twenty-third Jaina teacher, Parsva, ...

The twenty-third Jaina teacher, Parsva, the immediate predecessor of Mahavira enjoined on his disciples four great vows. To these Mahavira addes which of the followings as the fift

Evaluate the volume and surface area of a rectangular solid, Evaluate the v...

Evaluate the volume and surface area of a rectangular solid: Calculate the volume & surface area of a rectangular solid along with a =   3", b = 4", & c = 5".  Solution:

How many different combinations could she form these item, Wendy has 5 pair...

Wendy has 5 pairs of pants and 8 shirts. How many different combinations could she form with these items? Multiply the number of choices for each item to find out the number of

Power regression, how can i solve a multi variable power regression equatio...

how can i solve a multi variable power regression equation..? EX: y=a*(x1^b)*(x2^c).... i need to solve with 4 variable....

Interpretation of r – problems in interpreting r values, Interpretation of ...

Interpretation of r - Problems in interpreting r values A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that th

Determine a meet b and a join b, Given A and B                 A =  |  1...

Given A and B                 A =  |  1  0  1  |         B =   |  1  1  0  |                       |  1  1  0  |                 |  0  1  1  |                       |  0

The mean value theorem for integrals, The Mean Value Theorem for Integrals ...

The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin

Show inverse trigonometric functions, Q. Show Inverse Trigonometric Functio...

Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.

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