Finding Odz online. How to find the domain of definition of mathematical functions? Range of acceptable values ​​– there is a solution

A function is a model. Let's define X as a set of values ​​of an independent variable // independent means any.

A function is a rule with the help of which, for each value of an independent variable from the set X, one can find a unique value of the dependent variable. // i.e. for every x there is one y.

From the definition it follows that there are two concepts - independent a variable (which we denote as x and can take any value) and a dependent variable (which we denote as y or f(x) and is calculated from the function when we substitute x).

FOR EXAMPLE y=5+x

1. Independent is x, which means we take any value, let x=3

2. Now let’s calculate y, which means y=5+x=5+3=8. (y depends on x, because whatever x we ​​substitute, we get the same y)

The variable y is said to functionally depend on the variable x and is denoted as follows: y = f (x).

FOR EXAMPLE.

1.y=1/x. (called hyperbole)

2. y=x^2. (called parabola)

3.y=3x+7. (called straight line)

4. y= √ x. (called parabola branch)

The independent variable (which we denote by x) is called the function argument.

Function Domain

The set of all values ​​that a function argument takes is called the function's domain and is denoted D(f) or D(y).

Consider D(y) for 1.,2.,3.,4.

1. D (у)= (∞; 0) and (0;+∞) //the whole set real numbers, except zero.

2. D (y)= (∞; +∞)//all number of real numbers

3. D (y)= (∞; +∞)//all number of real numbers

4. D (y)= ∪∪; edited by S. A. Telyakovsky. - 17th ed. - M.: Education, 2008. - 240 p. : ill. - ISBN 978-5-09-019315-3.