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 the domain of definition of a function f(x): the set of values x which exists through f.

Answers to Questions

How to calculate the domain of definition of a function?

To calculate the definition set of a function in \( \mathbb{R} = ]-\infty ; +\infty [ \) look at the values for which the function is not defined. I.e, the values of \( x \) such as (\( f(x) \) do not exists. There are generally 3 main cases of undefined values (for real functions):

- division by \( 0 \) (null denominator), since \( 0 \) has no inverse

- negative square root: \( \sqrt{x} \) is defined only for \( x \ge 0 \)

- negative logarithm: \( \log(x) \) is defined only for \( x > 0 \)

dCode will compute and check the values without inverse by the function \( f \) and return the corresponding interval for the domain of the function.

Example: Consider \( f(x) = \sqrt{1-2x} \), since a root can not be negative, calculate the values such that \( 1-2x \ge 0 \iff x \le 1/2 \). Thus \( f(x) \) exists if and only if \( x \le 1/2 \). The domain of definition can be written \( D = ]-\infty; 1/2] \)

What is an antecedent?

Consider a function y = f (x) then the number y is called the image of x, and x is called an antecedent of y with the function f in the definition domain D.

Ask a new question

Source code

dCode retains ownership of the source code of the script Domain of Definition 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 Domain of Definition of a Function script for offline use, check contact page !

dCode uses cookies to customize the site content, analyze user behavior and adapt dCode to your use. Some data is stored and collected for advertising purposes and may be shared with our partners. OK