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

Example of method of elimination, Example    Solve each of the following sy...

Example    Solve each of the following systems of equations.              5x + 4 y = 1              3x - 6 y = 2 Solution It is the system in the previous examples wh

Linear equations, how do I solve the equation 0.6(x+60)+0.2x=52

how do I solve the equation 0.6(x+60)+0.2x=52

Ratios, Lee is taking some friends on a picnic. They''ll need to follow a p...

Lee is taking some friends on a picnic. They''ll need to follow a path to get to the picnic spot. A map of the path is based on a scale of 1:30,000, in cm. If the path is 12 cm on

Building equations, Mr. Rodriquez comments on a recent test. "well, the cla...

Mr. Rodriquez comments on a recent test. "well, the class average on the test is exactly 83. if I take away the best score, the average is exactly 82." if there are 16 students in

Math104, financial Project. Five years ago , you bought a house for $171,00...

financial Project. Five years ago , you bought a house for $171,000, with a down payment of $30,000, which meant you took out a loan for $141,000.Your interest rate was 5.75% fixed

Vertical shifts transformations, By using transformations sketch the graph ...

By using transformations sketch the graph of the given functions.                        g ( x ) = x 2 + 3 Solution Here the first thing to do is graph the function wit

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