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

Set, {a|a=9 ,a=N,a

{a|a=9 ,a=N,a

Algebra 2, How do I take two points, the rise and run, and produce an algeb...

How do I take two points, the rise and run, and produce an algebraic equation?

Cube of a binomial, how can we solve if the given is negative?

how can we solve if the given is negative?

Equations with radicals, The title of this section is perhaps a little misl...

The title of this section is perhaps a little misleading.  The title appears to imply that we're going to look at equations which involve any radicals.  However, we are going to li

Determine dimensions of the field using quadratic equation, we are going to...

we are going to fence into a rectangular field & we know that for some cause we desire the field to have an enclosed area of 75 ft2. We also know that we desire the width of the fi

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