Determine the inverse function f ( x ), Mathematics

Assignment Help:

Given f ( x ) = 3x - 2 determine     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 in fact start with this as we know what we have to get. This will work as a nice verification of the procedure.

Hence, let's get started. We'll replace first f ( x ) with y.

                                                    y = 3x - 2

Next, replace all of the x's along with y and all y's with x.

                                                     x = 3 y - 2

Now, solve out for y.

x + 2 = 3 y

1/3 ( x + 2) = y

Lastly 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 previous section, though; really we have to follow the procedure so we'll do that here. It doesn't matter which one from two that we verify we just have to check one of them.  This time we'll check 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

                         = x


Related Discussions:- Determine the inverse function f ( x )

Pemdas, what is the answer using pemdas (32 divided into 4)+3

what is the answer using pemdas (32 divided into 4)+3

Transportation problem, 12. List the merits and limitations of using North ...

12. List the merits and limitations of using North West corner rule.

Toplogy, Let 0 ! V1 !    ! Vk ! 0 be a long exact sequence of vector spa...

Let 0 ! V1 !    ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.

Circls, in a given figure a,b,c and d are points on a circle such that ABC ...

in a given figure a,b,c and d are points on a circle such that ABC =40 and DAB= 60 find the measure of DBA

Complex number, The points A,B,C and D represent the numbers Z1,Z2,Z3 and Z...

The points A,B,C and D represent the numbers Z1,Z2,Z3 and Z4.ABCD is rhombus;AC=2BD.if  Z2=2+i ,Z4=1-2i,find Z1 and Z3 Ans) POI of diagonals: (3-i)/2. Using concept of rotation:

Descrbe about arithmetic and geometric sequences, Descrbe about Arithmetic ...

Descrbe about Arithmetic and Geometric Sequences? When numbers are listed according to a particular pattern, we call the list a sequence. In a sequence, the numbers are separat

Last year a math textbook cost $54 what is this years cost, Last year, a ma...

Last year, a math textbook cost $54. This year the cost is 107 percent of what it was last year. What is this year's cost? a. $59.78 b. $57.78 c. $61.00 d. $50.22 To ?nd out

Geometric , a part of a line with two end points.

a part of a line with two end points.

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