Find the inverse of a given function, Algebra

Assignment Help:

Given f ( x ) = 3x - 2 find 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 really start with this as we know what we must get. it will work as a nice verification of the procedure.

We'll first replace f ( x ) with y.

                                           y = 3x - 2

Next, replace all x's with y & all y's with x.

                                            x =3 y - 2

Now, solve out for y.

x + 2 = 3 y

1 /3 (x + 2) = y

x/3 + 2/3=y

At last 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 earlier section; though, we actually should follow the procedure so we'll do that here. It doesn't issue which of the two that we verify we just have to check one of them.  This time we'll verify 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

                         =


Related Discussions:- Find the inverse of a given function

Which quantity is bigger?, Sam is twice as old as John was two years ago. I...

Sam is twice as old as John was two years ago. If the difference between their ages be 2 years, how old is Sam today?

Method to solve systems, There is a third method that we'll be looking at t...

There is a third method that we'll be looking at to solve systems of two equations, but it's a little more complicated and is probably more useful for systems with at least three e

Equations, solve the system of equations using the substitution method. y+5...

solve the system of equations using the substitution method. y+5x=10 -10x+3y=5

Proportions, A kilometer is about 5/8 mile.About how many miles are in 4 2/...

A kilometer is about 5/8 mile.About how many miles are in 4 2/5 kilometers? How would I set a proportion?

Factorisation, http://www.transtutors.com/live-online-tutor/math-help/

http://www.transtutors.com/live-online-tutor/math-help/

I dont grasp it, please help I just done grasp algebra

please help I just done grasp algebra

HELP, imagine you are a health professional interestedin the effects of med...

imagine you are a health professional interestedin the effects of medication on the diastolic blood pressure of adult women. for a certain drug being investigated, you find that fo

Interval notation, I can find what x means I just cant do the interval nota...

I can find what x means I just cant do the interval notation correctly

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