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

Integrated algebra me 1, identify the sample and suggest a population from ...

identify the sample and suggest a population from which it was selected. then classify the sample as sample, stratified, or systematic. explain your reasoning. 1} an insurance comp

Distance, If a jet can travel 600 mph, how long in second will it take the ...

If a jet can travel 600 mph, how long in second will it take the jet to travel 5 miles?

First form of the parabola, Let's go through first form of the parabola. ...

Let's go through first form of the parabola.                     f ( x ) = a ( x - h ) 2  + k There are two pieces of information regarding the parabola which we can instant

Sketch the graph of ellipses, Example:   Sketch the graph of ellipses.  ...

Example:   Sketch the graph of ellipses.                                  (x +2) 2 /9 + ( y - 4) 2 /25 =1 Solution So, the center of this ellipse is ( -2, 4) and as usua

Domain and range, Consider the function y = 2x. the domain is restricted to...

Consider the function y = 2x. the domain is restricted to 0 = x = 4, what is the range of this function

Radical Expressions, An object 4.8 feet tall casts a shadow that is 14.4 fe...

An object 4.8 feet tall casts a shadow that is 14.4 feet long. How long in feet would the shadow be for an object which is 16.8 feet tall?

Calculate the greatest common divisor, Question 1: (a) Describe a binar...

Question 1: (a) Describe a binary operation on a set S. (b) Give the definition of a group. (c) State whether the following statements are TRUE or FALSE. Justify your

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