Find the inverse of a given function, Algebra

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

                         =

Posted Date: 4/8/2013 1:27:04 AM | Location : United States







Related Discussions:- Find the inverse of a given function, Assignment Help, Ask Question on Find the inverse of a given function, Get Answer, Expert's Help, Find the inverse of a given function Discussions

Write discussion on Find the inverse of a given function
Your posts are moderated
Related Questions
Solve out the following system of equations by using augmented matrices. 3x - 3 y - 6 z = -3 2x - 2 y - 4 z = -2 -2x + 3 y + z = 7 Solution Notice that this system


Augmented Matrix Previously we saw that there were some special cases in the solution to systems of two equations. We illustrated that there didn't need to be a solution at al



in her last gymnastics competition Keri scored a 5.6 on the floor exercise, 5.85 on the vault and 5.90 on the balance beam. what was keri''s total?

find the opposite number of -8?

the sum of four consecutive even integers is 2 more than five times the first integer.find the smallest integer

find the inverse function f(x)=log12(x)