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

Identifying the property, if I have the equation 3(x+4y)+5(2x-y)an then I c...

if I have the equation 3(x+4y)+5(2x-y)an then I change it into (3x+12y)+(10x-5y) what property is it

Sketch the graph parabolas, Sketch the graph parabolas. f (x ) = 2 ( x +...

Sketch the graph parabolas. f (x ) = 2 ( x + 3) 2   - 8 Solution In all of these we will just go through the procedure given above to determine the required points and t

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

.., 2 bicyclist riding on a circular track start at the same time. one can ...

2 bicyclist riding on a circular track start at the same time. one can make it around the track in 8 min. the other takes 10 min. how long will it take the faster bicyclist to catc

Kelsey, my homework instructions are "solve by factoring" and one of the pr...

my homework instructions are "solve by factoring" and one of the problems is 2x^2+9x=0

Solve the equation using absolute value equations, Example: Solve following...

Example: Solve following.                      | 10 x - 3 |= 0   Solution Let's approach this one through a geometric standpoint. It is saying that the quantity in th

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