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.

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day! You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

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.

Answers to Questions

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 \( f \) whose formula is known, 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 \( y = a \).

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 \( x \).

Ask a new question

Source code

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 given for free. So if you need to download the online Preimage of a Function script for offline use, check contact page !