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 )

Math help, I need help with direct variation between x and y

I need help with direct variation between x and y

What is sherman''s pulse rate in beats per minute, Sherman took his pulse f...

Sherman took his pulse for 10 seconds and counted 11 beats. What is Sherman's pulse rate in beats per minute? A 10 second count is 1/6 of a minute. To find out the number of be

Arithmetic/Geometric Sequences and Binomial Expansion, Find the 35th term o...

Find the 35th term of the sequence in which a1 = -10 and the common difference is 4.

MARKET TARGETING STATERGIES, A MANUFACTURING UNIT IS INTERESTED IN DEVELOPI...

A MANUFACTURING UNIT IS INTERESTED IN DEVELOPING A BENEFIT SEGMENTATION OF THE CAMERA MARKET. SUGGEST SOME MAJOR BENEFIT SEGMENT WITH MARKET TARGETING STRATEGIES?

Vectors, apllication in business and economics

apllication in business and economics

Interpretations of definite integral, Interpretations of Definite Integral ...

Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini

Applications of markov chains in business, please help me in my assignment,...

please help me in my assignment, explain Applications of Markov Chains in Business.

Arithmetic progressions, ARITHMETIC PROGRESSIONS: One  of the  endlessly a...

ARITHMETIC PROGRESSIONS: One  of the  endlessly alluring  aspects  of mathematics  is  that its thorniest  paradoxes have  a  way  of blooming  into  beautiful  theories Examp

Trigonometry, how to work out consumer arithmetic?

how to work out consumer arithmetic?

Calculus level 2, the first question should be done using the website given...

the first question should be done using the website given (www.desmos.com/calculator )and another good example to explain using the graph ( https://www.desmos.com/calculator/ydimzr

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