Tool to calculate preimage(s) (antecedents) by a function. The preimage of a value z by the function f are all the values for which the function f(x)=z.

Preimage of a Function - dCode

Tag(s) : Functions, Geometry

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

**From the definition of the function**

Finding the **preimage**(s) of a value $ a $ by a function $ f $ is equivalent to solving equation $ f(x) = a $.

__Example:__ Calculating the **preimage** of $ 1 $ by the function affine $ f(x) = 2x + 1 $ is to solve $ 2x + 1 = 1 \iff x = 0 $. So the fiber of $ 1 $ by $ f $ is $ 0 $

__Example:__ Find the **preimage** of $ 4 $ by the 2nd degree polynomial function $ g(x) = x^2 $. Solve the equation $ x^2 = 4 \ iff x \pm 2 $. So the **preimages** of $ 4 $ by $ g $ are $ -2 $ and $ 2 $

**From the curve of the function**

Finding the **preimage**(s) of a value $ a $ by a function $ f $, which has a known curve, is equivalent to find the abscissae of the intersection(s) of the curve with the ordinate line $ y = a $.

If a function $ f $ is such that $ f(x) = a $, the image of $ x $ by the function $ f $ is $ a $, and the **preimage** of $ a $ by the function $ f $ is $ x $.

Hash functions are combinations of nonlinear functions specifically created so that their antecedents are not easily computable. It is generally faster to calculate from the function f all the pairs (x, a) (or as much as possible, where the most probable) and to compare with the value of the antecedent sought.

dCode retains ownership of the online "Preimage of a Function" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Preimage of a Function" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Preimage of a Function" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Preimage of a Function" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

Please, check our dCode Discord community for help requests!

NB: for encrypted messages, test our automatic cipher identifier!

preimage,function,equation,fiber,value

Source : https://www.dcode.fr/function-preimage

© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲
Thanks to your feedback and relevant comments, dCode has developed the best 'Preimage of a Function' tool, so feel free to write! Thank you!