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

Critical point of exponential functions and trig functions, Critical point ...

Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example:  find out all the critical points for the

Lim.., how can solve limits

how can solve limits

Math, #questionQn 1- An analysis of monthly wages of workers of two organi...

#questionQn 1- An analysis of monthly wages of workers of two organizations Alia LLC and Asila LLC yielded the following results. Alia LLC Asila LLC Average monthly wages 60

Retail price index, Retail price index This is weighted average of pri...

Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp

PDE, Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ...

Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket

Linear programming , A paper mill produces two grades of paper viz., X and ...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Integraton, how to find area under a curve

how to find area under a curve

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