Search for a tool
Preimage of a Function

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.

Results

Preimage of a Function -

Tag(s) : Functions, Geometry

Share
dCode and more

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!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

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

# Preimage of a Function

## Preimage Calculator

 Global domain for the function Reals R Integers Z Complex C

### How to calculate a preimage of a function?

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 $y = a$.

### What is the difference between image and preimage?

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 $x$.

### How to find the preimage of a hash function?

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.

## Source code

dCode retains ownership of the "Preimage of a Function" source code. Except explicit open source licence (indicated 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, or API access for "Preimage of a Function" are not public, same for offline use on PC, tablet, iPhone or Android !
The copy-paste of the page "Preimage of a Function" or any of its results, is allowed as long as you cite the online source https://www.dcode.fr/function-preimage
Reminder : dCode is free to use.

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!