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#1 2016-07-28 13:34:46

MathsIsFun
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Registered: 2005-01-21
Posts: 7,660

Inverse Functions

On this page: Inverse Functions

I have f(x) becoming f-¹(y)

But a reader has suggested it should be f-¹(x)   

It would certainly be simpler not swapping y for x. What is correct do you think?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2016-07-28 14:29:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Inverse Functions

Hi;

I think the f-¹(y) is more prevalent and the one I would prefer.

https://en.wikipedia.org/wiki/Inverse_function almost half way down the page in the second column of the table.

Also, in a video at the Khan academy I was watching he used your same notation. But, notation ain't my strong point so wait for more advice.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-07-28 16:51:15

ganesh
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Registered: 2005-06-28
Posts: 23,102

Re: Inverse Functions

Hi MathsIsFun;

In my opinion, f-¹(y) is the better choice; I agree with the views of bobbym.

The part of the page 'Inverses of Common Functions' serves as a reckoner.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#4 2016-07-28 18:32:30

thickhead
Member
Registered: 2016-04-16
Posts: 1,082

Re: Inverse Functions

That depends on definition.
If you define

then

If
then


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#5 2016-07-29 09:57:14

MathsIsFun
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Registered: 2005-01-21
Posts: 7,660

Re: Inverse Functions

Thanks Guys!

I found Wolfram uses f-¹(x): http://mathworld.wolfram.com/InverseFunction.html

It would be nice to simplify the page to f-¹(x) ... but in the intro I say "So the inverse of:   2x+3   is:   (y-3)/2" and that does not sit well with using f-¹(x)

Nor with the table of inverses as ganesh mentions.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#6 2016-07-29 10:32:56

RetiredPuzzleMathNerd
Member
Registered: 2016-07-29
Posts: 1

Re: Inverse Functions

I'm the reader that made the suggestion. I based it on how the process of inverting a function was taught in the Blitzer's textbook, Algebra and Trigonometry, 5th Edition, and in MyMathLab, and finally because, in these days that we can teach students to graph both functions on a graphing calculator, not all calculators are able to graph inverse function, x in terms of y.

On the TI-84 Plus series of calculators, I can only graph (X = constant) functions. I cannot graph (X = Y²).

Anyway, as I went through those problems, I did the work f(x) and f-¹(x) so that I did not have to manually graph a y=x equation, then swap the axes to see the inverse.

It may be that the major textbooks are changing to emphasizing  f-¹(x) because of the advent of graphing calculators in the last decade (or however long it's been) that cannot graph  f-¹(y). (I have only tested this on the TI-84 Plus C Silver Edition and on the TI-84 Plus CE. I have not checked to see if my HP Prime can graph x=y equations.

P.S. Hi, Ganesh, if you are the Ganesh in India that I share puzzles with.

John

Last edited by RetiredPuzzleMathNerd (2016-07-29 10:33:57)

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#7 2016-07-29 10:59:44

MathsIsFun
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Registered: 2005-01-21
Posts: 7,660

Re: Inverse Functions

The "graphing calculator" reasoning might be why Wolfram (ie Mathematica) uses  f-¹(x)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#8 2016-07-29 11:24:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Inverse Functions

Hi;

That is Eric's private page it does not necessarily represent the viewpoint of Wolfram.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2016-07-29 15:50:37

thickhead
Member
Registered: 2016-04-16
Posts: 1,082

Re: Inverse Functions

Better would be


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#10 2016-07-29 20:08:10

bob bundy
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Registered: 2010-06-20
Posts: 8,082

Re: Inverse Functions

Here's my opinion:  If f is a function then f(minus one) is commonly used to denote the inverse function.  f(x) and f(any other letter) are the same function ... just a different variable.  On that page the inverse function is (y-3)/2 so the variable is y.  That means

is correct and changing to x would be wrong as it's not given as a function of x.

But it would be ok to go on to say

If your calculator will only plot y as a function of x then this is how you'd have to get a graph.

This shouldn't be a problem for anyone who has got that far with their mathematical studies.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#11 2016-07-30 11:49:31

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,660

Re: Inverse Functions

Thanks everyone!

I will leave the page as it is until I can think of a way to simplify it without straying into "y=2x+3 becomes y=(x-3)/2" territory.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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