Determine the inverse function f ( x ), Mathematics

Assignment Help:

Given f ( x ) = 3x - 2 determine     f -1 ( x ) .

Solution

Now, already we know what the inverse to this function is as already we've done some work with it.  Though, it would be nice to in fact start with this as we know what we have to get. This will work as a nice verification of the procedure.

Hence, let's get started. We'll replace first f ( x ) with y.

                                                    y = 3x - 2

Next, replace all of the x's along with y and all y's with x.

                                                     x = 3 y - 2

Now, solve out for y.

x + 2 = 3 y

1/3 ( x + 2) = y

Lastly replace y with f -1 ( x ) .

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

Now, we have to verify the results.  Already we took care of this in the previous section, though; really we have to follow the procedure so we'll do that here. It doesn't matter which one from two that we verify we just have to check one of them.  This time we'll check that ( f o f -1 )( x ) = x is true.

 ( f o f -1 )( x ) = f [ f -1 ( x )]

                        =f [ x/3 + 2/3 ]

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

                            = x +2 - 2

                         = x


Related Discussions:- Determine the inverse function f ( x )

Ratio, ther are 162 student in a school.20 of them are girls .how many are ...

ther are 162 student in a school.20 of them are girls .how many are boy

Decision trees and bayes theory, Decision Trees And Bayes Theory This m...

Decision Trees And Bayes Theory This makes an application of Bayes' Theorem to resolve typical decision problems. It is examined a lot so it is significant to clearly understan

Calculate expected average time , A car was machine washes every car in 5 m...

A car was machine washes every car in 5 minutes accurately. It has been calculated that customers will arrive as per to a Poisson distribution at an average of 8 per hour. Calculat

What is graphing statistics explain , What is Graphing Statistics explain ?...

What is Graphing Statistics explain ? The number of times that an event occurs is called its frequency. One of the ways that you can compare or display different frequencies is

Sum, As1212uestion #Minimum 100 words accepted#

As1212uestion #Minimum 100 words accepted#

Objectives of addition and subtraction, Objectives After going throu...

Objectives After going through this unit, you should be able to 1. explain the processes involved ih addition and subtraction; 2. plan and execute activities that woul

Algebra, Evaluate: 30 - 12÷3×2 =

Evaluate: 30 - 12÷3×2 =

Approximating definite integrals - integration techniques, Approximating De...

Approximating Definite Integrals - Integration Techniques In this section we have spent quite a bit of time on computing the values of integrals. Though, not all integrals can

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