Finding the inverse of a function , Mathematics

Assignment Help:

Finding the Inverse of a Function : The procedure for finding the inverse of a function is a rather simple one although there are a couple of steps which can on occasion be somewhat messy.  Following is the process

Given the function f ( x ) we desire to determine the inverse function, f -1 ( x ) .

a. Firstly, replace f ( x ) with y. It is done to make the rest of the procedure easier.

b. Replace every x to a y and replace every y to an x.

c. Solve out the equation from Step 2 for y. it is the step where mistakes are most frequently made so be careful with this step.

d. Replace y with f -1 ( x ) .  In other terms, we've managed to determine the inverse at this point!

e. Check your work by verifying that (f o f -1 )( x ) = x and ( f -1 + f )( x ) = x are both true. Sometimes this work can be messy making it simple to make mistakes so again be careful.

That's the procedure. Most of the steps are not all that bad although as mentioned in the procedure there are a couple of steps that we actually have to be careful with as it is easy to commit mistakes in those steps.

In the verification step technically we really do have to check that both ( f o f -1 )( x ) = x and ( f -1 o f )( x ) = x are true.  For all of the functions which we are going to be looking at in this course if one is true then the other will also be true.  Though, there are functions for which it is probable for only one of these to be true. It is brought up since in all the problems here we will be just verifying one of them.  We just have to always remember that technically we have to check both.


Related Discussions:- Finding the inverse of a function

Complex root - fundamental set of solutions, Example : Back into the comple...

Example : Back into the complex root section we complete the claim that y 1 (t ) = e l t cos(µt)        and      y 2 (t) = e l t sin(µt) Those were a basic set of soluti

Trigonometry, how to change sin 24 degree in digits?

how to change sin 24 degree in digits?

6th grade, what is the length of a line segment with endpoints (-3,2) and (...

what is the length of a line segment with endpoints (-3,2) and (7,2)?

Determine the measure of angle, Using the expample provided below, if m∠ABE...

Using the expample provided below, if m∠ABE = 4x + 5 and m∠CBD = 7x - 10, Determine the measure of ∠ABE. a. 155° b. 73° c. 107° d. 25° d. ∠CBD and ∠ABE are vert

Jordan needs help, carlie is now fivetimes as old as henry. in nine years ...

carlie is now fivetimes as old as henry. in nine years her age will be twice henry''s age then. how old is carly now

Trigonometry, if theta is a positive acute angle and 2sin theta +15cos squ...

if theta is a positive acute angle and 2sin theta +15cos square theta=7 then find the value of cot theta

Differentiation of a formula with two variables, I would like to calculate ...

I would like to calculate the high point of a mathematical formula with two unknown variables. At the same time I made the 1st derivation of the function. How can I best program th

5, what is a variable

what is a variable

Melissa is four times if jim is y years old, Melissa is four times as old a...

Melissa is four times as old as Jim. Pat is 5 years older than Melissa. If Jim is y years old, how old is Pat? Start along with Jim's age, y, because he appears to be the young

What was the planes average speed, A ?ight from Pittsburgh to Los Angeles t...

A ?ight from Pittsburgh to Los Angeles took 5 hours and covered 3,060 miles. What was the plane's average speed? Find out the rate at that Susan is traveling through dividing h

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