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*!

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.

**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 \( f \) whose curve is known is 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 simpler 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 source code of the script Preimage of a Function online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Preimage of a Function script for offline use on PC, iPhone or Android, ask for price quote on contact page !

preimage,function,equation,fiber,value

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

© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲