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

Algebra, To find the calorie density (D) in calories per ounce of food that...

To find the calorie density (D) in calories per ounce of food that contains c carories and weight w ounces is given by D=C/w

Backtracking equations, I need some help with Backtracking equations.I have...

I need some help with Backtracking equations.I have a quiz tomorrow, and i was hoping that you guys could help.

Graphing, the problem is 6x+3y=-24. is tells me to graph using y=mx+b forma...

the problem is 6x+3y=-24. is tells me to graph using y=mx+b format but i don''t know how to get to that point.

Algerbra I, I have 4 word problem on my review that I cant figure out. Can ...

I have 4 word problem on my review that I cant figure out. Can you help me?

Statistics, what are the two types of ogive curves

what are the two types of ogive curves

Integers, how to find the distance between -2 and 3 on a number line

how to find the distance between -2 and 3 on a number line

Elem mat., A store sells cashews for $3.00 per pound and pecans for $8.00 p...

A store sells cashews for $3.00 per pound and pecans for $8.00 per pound. How many pounds of cashews and how many pounds of pecans should you mix to make a 50-lb mixture costing $4

Example of synthetic division, Using synthetic division do following  divis...

Using synthetic division do following  divisions. Divide 2x 3 - 3x - 5  by x + 2 Solution Okay in this case we have to be a little careful here. We have to divide by a

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