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

Infinity, Are there more rational numbers than integers?#

Are there more rational numbers than integers?#

Exponential functions, The exponential functions are useful for descr...

The exponential functions are useful for describing compound interest and growth. The exponential function is defined as:          y = m. a x where '

Show that the angles subtended at the centre , A circle touches the sides o...

A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.

Derivatives for logarithm, Logarithm Functions : Now let's briefly get the...

Logarithm Functions : Now let's briefly get the derivatives for logarithms.  In this case we will have to start with the following fact regarding functions that are inverses of ea

Discovery, i have discovered a formula for finding the radius at any point ...

i have discovered a formula for finding the radius at any point of the graph have i done a good job

Solid geomerty, find the equation to the sphere through the circle xsqaure+...

find the equation to the sphere through the circle xsqaure+ysquare+zsquare+=9 , 2x+3y+4z=5

Application of linear function, four times an unknown number is equal to tw...

four times an unknown number is equal to twice the sum of five and that unknown number

Houses having the floor , Suppose you are in the market for a new home and ...

Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative informs you that the

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