Search for a tool
Domain of Definition of a Function

Tool to calculate the domain of definition of a function f(x): the set of values x which exists through f (from the equation of the function or its curve).

Results

Domain of Definition of a Function -

Tag(s) : Functions

Share dCode and you

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!

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Domain of Definition of a Function tool. Thank you.

# Domain of Definition of a Function

## Calculation of a Function's Domain of Definition

 Solving Domain Set R (Reals) C (Complex)

Tool to calculate the domain of definition of a function f(x): the set of values x which exists through f (from the equation of the function or its curve).

### 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 exists and those for which it does not exist, ie the values of $x$ such that $f(x)$ is not defined.

'From the equation of the function'

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: Take $f(x) = \sqrt{1-2x}$, 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 $D = ]-\infty; 1/2]$

'From the curve of the function'

It is a question of looking at the values for which the curve has no point. Either because there is a vertical asymptote, or because there is simply no value.

### What does domains R+ or R- or R* means?

$\mathbb{R}$ is the domain of real numbers

$\mathbb{R^+}$ (R plus) is the domain of positive real numbers (0 included)

$\mathbb{R^-}$ (R moins) is the domain of negative real numbers (0 included)

$\mathbb{R^*}$ (R étoile) is the reals domain excluding the value 0.

$\mathbb{R_+^*}$ (R étoile plus) is the domain of positive real numbers (0 exclus)

$\mathbb{R_-^*}$ (R étoile moins) is the domain of negative real numbers (0 exclus)

### What is an antecedent?

If 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.

### What is the existence domain of a function?

The domain of existence and the domain of definition of a function are identical, it is the same concept.

## 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 released for free. To download the online Domain of Definition of a Function script for offline use on PC, iPhone or Android, ask for price quote on contact page !