Definition of inverse functions, Mathematics

Assignment Help:

Definition of inverse functions :  Given two one-to-one functions f ( x ) and g ( x ) if ( f o g ) ( x ) = x  AND  ( g o f ) ( x ) = x

then we say that f ( x ) & g ( x ) are inverses of each other. More particularly we will say that g ( x ) is the inverse of f ( x ) and denote it by

                                                g ( x ) = f -1 ( x )

Similarly we could also say that f ( x ) is the inverse of g ( x) and indicate it by

                                              f ( x ) = g -1 ( x )

The notation that we employ really based upon the problem.  In most of the cases either is acceptable. For the two functions which we begun this section along with we could write either of the given two sets of notation.

f ( x ) = 3x - 2                                                     f -1 ( x ) = x/3 +2/3

g ( x ) = x/3 + 2/3                                                g -1 ( x ) = 3x - 2

 Be careful along with the notation for inverses. The "-1" is NOT an exponent in spite of the fact that is sure does look like one! While dealing along with inverse functions we've got to remember that

                                                f-1(x)   ≠1/f(x)

It is one of the more common mistakes which students make while first studying inverse functions.


Related Discussions:- Definition of inverse functions

What is pythagorean triples, What is Pythagorean Triples? A set of thre...

What is Pythagorean Triples? A set of three numbers a, b, and c that can satisfy the equation A 2 +b 2 = c 2 , is called a Pythagorean triple. The following is a list of

3-d coordinate system - three dimensional spaces, The 3-D Coordinate System...

The 3-D Coordinate System We will start the chapter off with a quite brief discussion introducing the 3-D coordinate system and the conventions that we will be utilizing.  We

Sample space, Sample Space is the totality of all possible out...

Sample Space is the totality of all possible outcomes of an experiment. Hence if the experiment was inspecting a light bulb, the only possible outcomes

Age problem, three years ago,Rica was thrice as old as dandy.Three years he...

three years ago,Rica was thrice as old as dandy.Three years hence,she will be twice as old.Find their present.

Word problems fraction, Savannah''s mom made a fruit smoothie that tasted s...

Savannah''s mom made a fruit smoothie that tasted so good. She put in one-fourth of a cup of diced apples, one-fifth of a cup of sliced oranges, along with half of a cup of yogurt

#titlefunction.., provide a real-world example or scenario that can be expr...

provide a real-world example or scenario that can be express as a relation that is not a function

What was the temperature at midnight, The temperature at 6 P.M. was 31°F. T...

The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight? Visualize a number line. The drop from 31° to 0° is 31°. There

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