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 $
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.