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 )

Exponets, what does the three mean in the power ?

what does the three mean in the power ?

Evaluate the following exponentials limit, Evaluate following limits. ...

Evaluate following limits. Solution: Let's begin this one off in the similar manner as the first part. Let's take the limit of each piece. This time note that since our l

Integration, ((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)

((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)

Integration, integral 0 to 4 integral 0 to y root of 9+ysquredxdy

integral 0 to 4 integral 0 to y root of 9+ysquredxdy

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Series is converges or diverges - limit comparison test, Determine if the f...

Determine if the following series converges or diverges by using limit comparison test. Solution To make use of the limit comparison test we require to find out a seco

Determine the inverse transform, Determine the inverse transform of each of...

Determine the inverse transform of each of the subsequent. (a)    F(s) = (6/s) - (1/(s - 8)) + (4 /(s -3)) (b)   H(s) = (19/(s+2)) - (1/(3s - 5))  + (7/s 2 ) (c)    F(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