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

The volume and surface area of this solid , The region bounded by y=e -x a...

The region bounded by y=e -x and the x-axis among x = 0 and x = 1 is revolved around the x-axis. Determine the volume and surface area of this solid of revolution.

Estimate percent of the babies born among 6 and 8.5 pounds, 25% of babies b...

25% of babies born at Yale New Haven Hospital weigh less than 6 pounds and 78% weigh less than 8.5 pounds. What percent of the babies born at Yale New Haven Hospital weigh among 6

Find out the radius of convergence, Example: Find out the radius of conver...

Example: Find out the radius of convergence for the following power series. Solution : Therefore, in this case we have, a n = ((-3) n )/(n7 n+1 )   a n+1 = (

Integration and differentiation, Integration and Differentiation Diffe...

Integration and Differentiation Differentiation deals along with the determination of the rates of change of business activities or merely the process of finding the derivativ

Example of mathematical operations, Example of mathematical operations: ...

Example of mathematical operations: Example: Solve the following equation: [2 .( 3 + 5) - 5 + 2] x 3 =  ________   Solution: a.         Perform operations with

Determine the property of partial ordered relation, Determine the property ...

Determine the property of Partial ordered relation Question: Partial ordered relation is transitive, reflexive and  Answer: antisymmetric

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