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

Prisms, how do i find the are of a triangular prism if the number that i mu...

how do i find the are of a triangular prism if the number that i multiply is an odd number and i have to divide by 2

Example of double inequalities, Now, let's solve out some double inequaliti...

Now, let's solve out some double inequalities. The procedure here is alike in some ways to solving single inequalities and still very different in other ways. As there are two ineq

Negative exponents, what is the proper way to state a negative exponent whe...

what is the proper way to state a negative exponent when dividing example 27exponent -2/3 divided by 27 exponent -1/3

Solve, 15+1/2x=0.60(20+x)

15+1/2x=0.60(20+x)

Percentage, Two sessions of swimming lessons were held at a pool. In the fi...

Two sessions of swimming lessons were held at a pool. In the first session 40 students attended. Of these 40 students 60% were girls. How many girls attended the first session of s

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