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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).

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Domain of Definition of a Function -

Tag(s) : Functions

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# 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 is not defined. I.e, the values of $$x$$ such as ($$f(x)$$ do not exists.

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 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.

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