Tool to calculate an image of a function. The image of a value z by the function f is the value of f(x) where x=z, also written f(z).
Image 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!
Image of a Function
Answers to Questions (FAQ)
What is an image by a function? (Definition)
The image $ y $ of the value $ x $ by the function $ f $ is $ y = f(x) $.
An image $ y $ exists if $ y $ belongs to the domain of definition of $ f $.
The image $ y $ by the function $ f $ is unique (there are never 2 images).
How to calculate an image of a function?
From the definition of the function
To find the image of a value $ a $ by a function $ f(x) $ whose formula/equation is known, is equivalent to compute $ f(x = a) = f(a) $.
Example: To calculate the image of $ 2 $ by the affine function $ f(x) = 3x + 1 $ is to compute $ 3 \times 2 + 1 = 7 $. So the image of $ 2 $ by $ f $ is $ f(2) = 7 $.
From the curve of the function
Finding the image of a value $ a $ by a function $ f $ whose curve is known, is to find the ordinate of the intersection of the curve with the abscissa line $ x = a $.
Example: Finding the image of $ 1 $ by the inverse function $ f(x) = 1/x $ is finding the intersection of the abscissa line $ x = 1 $ with the curve then go down to the corresponding ordinate: $ 1 $ so $ f(1) = 1 $.
What is the difference between image and preimage?
If a function $ f $ is such that $ f(x) = a $, the preimage of $ a $ by the function $ f $ is $ x $, and the image of $ x $ by the function $ f $ is $ a $.
What is a domain of definition of a function?
The domain of definition of a function is the image set of all possible images by the function.
Source code
dCode retains ownership of the "Image of a Function" source code. Except explicit open source licence (indicated Creative Commons / free), the "Image of a Function" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Image 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 "Image of a Function" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Image of a Function" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Image of a Function on dCode.fr [online website], retrieved on 2024-07-27,
