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

Homework, A toy manufacturer develops a formula to determine the demand for...

A toy manufacturer develops a formula to determine the demand for its product depending on the price in dollars. The formula is , where P is the price per unit and D is the number

Absolute value inequalities, In the earlier section we solved equations whi...

In the earlier section we solved equations which contained absolute values.  In this section we desire to look at inequalities which contain absolute values.  We will have to exami

LCD, I dont understand why the least common denominator to the problem (3/2...

I dont understand why the least common denominator to the problem (3/2x) minus (1/2(x+10)) equals 1 is 2x(x+10)

System of equation problem., Solve the system y = -x + 7 and y = -0.5(x - 3...

Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8

Factoring, factor out the greatest common fctor

factor out the greatest common fctor

7.5 Special Systems, Can you get me more questions to practice on this.

Can you get me more questions to practice on this.

School, Find the interest if: p = $8000, r = 6%, and t = 1 year

Find the interest if: p = $8000, r = 6%, and t = 1 year

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