From d8e0d5119a87330741c85ae4fc74668a81834267 Mon Sep 17 00:00:00 2001 From: hannelita Date: Sun, 5 Jul 2015 12:35:44 -0700 Subject: [PATCH 1/3] Inverse function definition --- README.md | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/README.md b/README.md index e1e087d..79b5149 100644 --- a/README.md +++ b/README.md @@ -722,6 +722,20 @@ Some tools like [flowtype](http://flowtype.org/) attempt to bring static typing Other languages, like Java, allow for true method overloading based on the static types of a function's input/output. This is closer to mathematics: two functions are not the same if they use a different *domain*. +### inverse function + +In mathematics, we have the formal concept of inverse function saying that for a function *f(x)*, it's inverse function, denoted as +![function2](http://latex.codecogs.com/svg.latex?f%5E%7B-1%7D%28x%29), where for each *x* belonging to the range of *f*, *f-1(x)* is defined to be the unique value of *y* in the domain of *f* satisfying *x = f(y)* + + + +Or, in s simplified way, + +![function2](http://latex.codecogs.com/svg.latex?y%3Df%5E%7B-1%7D%28x%29) is equivalent to +![function2](http://latex.codecogs.com/svg.latex?x%20%3D%20f%28y%29) + + + ## prime The prime symbol (`′`) is often used in variable names to describe things which are similar, without giving it a different name altogether. It can describe the "next value" after some transformation. From 559ff834fd0c8ef49f83274d129e7799979be4ed Mon Sep 17 00:00:00 2001 From: hannelita Date: Sun, 5 Jul 2015 13:24:29 -0700 Subject: [PATCH 2/3] Inverse functions implementations --- README.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 79b5149..aa75623 100644 --- a/README.md +++ b/README.md @@ -732,10 +732,16 @@ In mathematics, we have the formal concept of inverse function saying that for a Or, in s simplified way, ![function2](http://latex.codecogs.com/svg.latex?y%3Df%5E%7B-1%7D%28x%29) is equivalent to -![function2](http://latex.codecogs.com/svg.latex?x%20%3D%20f%28y%29) +![function2](http://latex.codecogs.com/svg.latex?x%20%3D%20f%28y%29). +Inverse functions are not restricted to polynomials, the concept also can be applied to transcendental functions (logarithms and trigonometric functions, for example). + +The algorithm to find an inverse function basically consists in changing substituting *x* with *y* and the opposite, *y* with *x*. + +The implementation, however, may vary. You usually do not see a single *function inverse*. Instead libraries tend to separate it by case, once the input varies a lot. Examples, we have a separate set for trigonometric inverse functions on [math.js](http://mathjs.org/) - *tan()* and *atan()*, *sin()* and *asin()*, etc. + ## prime The prime symbol (`′`) is often used in variable names to describe things which are similar, without giving it a different name altogether. It can describe the "next value" after some transformation. From 79255ef2d36a9d338b7f2f3d4eb59661754a52a8 Mon Sep 17 00:00:00 2001 From: hannelita Date: Sun, 5 Jul 2015 13:29:10 -0700 Subject: [PATCH 3/3] Updating contents --- README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/README.md b/README.md index aa75623..ecfa237 100644 --- a/README.md +++ b/README.md @@ -38,6 +38,7 @@ For simplicity, many of the code examples here operate on floating point values - [piecewise function](#piecewise-function) - [common functions](#common-functions) - [function notation `↦` `→`](#function-notation) + - [inverse functions](#inverse-functions) - [prime `′`](#prime) - [floor & ceiling `⌊` `⌉`](#floor--ceiling) - [arrows](#arrows)