Hawthorne - I removed the note because ex is defined for all complex numbers, and so is ln(x). (See, for example, Euler's formula.)
- Fair enough. Maybe someone cleverer than us both can find a way to make it both simple and precise.
Also, I think that there are a lot of people unfamiliar with the universal operator, and it makes the formula overly confusing. I really don't think one needs to be that precise for something that goes without saying, especially when it obscures the simplicity of the concept.
- you mean the ? Perhaps so - how about we replace it with good old fashioned English instead.
Perhaps the set operators can be separated from the main formula? Perhaps that part (along with the right and left inverse) can have it's own small section on the page? I think this would improve the page.
-User:Kevin_baas 2003.06.24
- The right and left inverse could be separated off if neccessary, although I think if care is taken with wording that stuff can be made to fit in here without making the page any harder to read. However the definition of inverse must include the composition both ways around. Otherwise it just isn't right.
- Yes, it must, I know.
- I think that the switch to English helped alot. I concede on the right and left inverse on account of this.
-User:Kevin_baas 2003.06.24
For example, x3 + x, at x = 2, equals 10; the inverse function equals 2, when x = 10. If one tries to find the derivative of f(x)−1, at x = 10, one might note that f ' −1(10) = 1 / f '[f −1(10)] = 1 / f '(2); and since f ' is 3x2 + 1; then, f ' −1(10) = 1 / [3(2)2 + 1] = 1 / 13. Indeed, f '(2) = 13; thus f '−1 should be 1 / 13.
Is this not correct? Pizza Puzzle
Do you calculate (f(x)−1)' or f−1(x)'? Your calculation is correct if it is the second case. Wshun
Well, Im not sure I understand your question; but, if this is correct, perhaps it should be reinserted to the article? Pizza Puzzle
The first symbol (f(x)−1)' means ((1/f(x))−1)' which equals -f '(x)/(f(x))2, not 1/f '(x). It seems that you are confused the symbol of pointwise inverse f(x)−1=1/f(x) with the symbol of inverse function f−1(x) Wshun.
Yes, but barring that issue (which can be easily corrected) is there any reason to exclude this example from the text? Pizza Puzzle
- The differentation section currently is missing examples. It would probably do good for it to have an example section with at least one example. -- Provided that the example is appropriate, uses the correct notation, and is clearly presented( i.e. inline formulas = bad, the steps are clearly shown, the example is simple and fundamental, the structure of the presentation is visually clear, ect.).
User:Kevin_baas 2003.06.26
For example, x3 + x, at x = 2, equals 10; the inverse function equals 2, when x = 10. If one tries to find the derivative of f(x)−1=1/f(x), at x = 10, one might note that f ' −1(10) = 1 / f '[f −1(10)] = 1 / f '(2); and since f ' is 3x2 + 1; then, f ' −1(10) = 1 / [3(2)2 + 1] = 1 / 13. Indeed, f '(2) = 13; thus f '−1 should be 1 / 13.
Any other corrections desired? Pizza Puzzle
Hawthorne- I really don't think that adds to it. What you did is:
1. make a sentence more complex
2. added new concepts into the mix which are
- a. unneccessary
- b. not defined on the page
3. put an example
- a. outside the example section
- b. before the definition
I think that it's important to first get the main concept across as quickly and directly as possible, and develop the detail and specifics afterwards.
-User:Kevin_baas 2003.06.26
- Opps! that change was made by pizza. sorry hawthorne! I should always check the history. pizza...
- (also, to be more specific, the part regarding 'arguments', refers to the definition of a function, and belongs there as well.)
-User:Kevin_baas 2003.06.26
For example, x3 + x, at x = 2, equals 10; the inverse function equals 2, when x = 10. If one tries to find the derivative of f(x)−1=1/f(x), at x = 10, one might note that f ' −1(10) = 1 / f '[f −1(10)] = 1 / f '(2); and since f ' is 3x2 + 1; then, f ' −1(10) = 1 / [3(2)2 + 1] = 1 / 13. Indeed, f '(2) = 13; thus f '−1 should be 1 / 13.
Any other corrections desired?
- We are not interested in the multiplicative inverse (1/x), but rather the functional inverse. Use the formula that I put at the bottom of the article.
-User:Kevin_baas 2003.06.26
I think this is the formula from the bottom, its an example of using that formula. Pizza Puzzle
- If it is, it is hard to see. Take the derivative of f(x), then take the reciprocal of that, ect. verify(e.g. show that at x = 2, y = 10.) only at the very end, not at the beginning, and only plug in numbers at the end. (before the verification) also, don't put the formulas inline. (First priorities are readability and organization.) Then I'll look at it again.
-User:Kevin_baas 2003.06.26
Isn't the derivative of x3 + x equal to 13 at x = 2? Pizza Puzzle
yes, it is. that's beside the point. -User:Kevin_baas 2003.06.26
no, its not besides the point. You are implying that there is something wrong with my example. Do you know what the inverse is to x3 + x? Pizza Puzzle
I am not implying anything. I am stating that there is something wrong with the way your example is presented. -User:Kevin_baas 2003.06.26
If there is nothing wrong with the factual content of the text, and your only problem is "presentation" then you should either fix the presentation yourself or admit that you really don't think its so important to fix. I certainly can't guess at how you would like it to look. Pizza Puzzle
That is why I explicitely listed what I felt was wrong with the presentation, in a very clear and objective manner, along with suggestions for improvements. Ofcourse, presentation is very important. It is the raison de'tere (reason for being) of this encyclopedia in general. I think that it is very important, as you know -- as I've written on your talk page, concurring with you. -User:Kevin_baas 2003.06.26
Right, but not of your "explicity explanations" of what is wrong with the presentation can really make sense. If I painted a picture, and you said "I think it should be more..."jazzy" that would be about as helpful. This is a wiki, anyone can edit anything. All Im asking is why was this example removed from the page, faulty math or incorrect facts is a reasonable reason to delete something; but, deleting it because it doesn't look good enough isn't a reason. The whole wiki doesnt look good enough, the presentation of every article needs to be improved, and the only way stuff gets improved is if its in the article where people are seeing it. Pizza Puzzle
Things like "do not put formulas inline" and "plug in the numbers at the end, not the beginning", are not very fuzzy concepts. The analogy would to a portrait would be "do not paint two objects in the same space" and "first, draw the lines, then fill them in with color". User:Kevin_baas 2003.06.26
Things like "do not put formulas inline" and "plug in the numbers at the end, not the beginning", are very fuzzy when "inline formulas" doesnt make any sense and I did plug the numbers in at the end, the end was at the beginning because its very short. Pizza Puzzle