Tool to calculate preimage(s) (antecedents) by a function for given value from the function expression.
Preimage of a Function - dCode
Tag(s) : Functions, Geometry
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Preimage of a Function
Preimage Calculator
Answers to Questions (FAQ)
What is a preimage by a function? (Definition)
The preimage of a value $ z $ by the function $ f $ are all the values for which the function $ f(x) = z $.
How to find a preimage of a function?
From the definition of the function (without graph)
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.
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