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. Any algorithm for the "Image of a Function" algorithm, applet or snippet or script (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or any "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.) or any database download or API access for "Image of a Function" or any other element are not public (except explicit open source licence like Creative Commons). Same with the download for offline use on PC, mobile, tablet, iPhone or Android app.
Reminder: dCode is an educational and teaching resource, accessible online for free and for everyone.
Cite dCode
The content of the page "Image of a Function" and its results may be freely copied and reused, including for commercial purposes, provided that dCode.fr is cited as the source.
Exporting the results is free and can be done simply by clicking on the export icons ⤓ (.csv or .txt format) or ⧉ (copy and paste).
To cite dCode.fr on another website, use the link:
In a scientific article or book, the recommended bibliographic citation is: Image of a Function on dCode.fr [online website], retrieved on 2025-04-16,
