Function is called compliance which compares to each number x from some set set y singular. The set of values x is called a function range of definition. I.e. this set of all permissible values of an argument (x) at which the y=f (x) function is defined (exists).
Instruction
1. If at function there is a fraction, and the denominator contains variable (x), then the denominator of fraction should not be equal to zero since differently such fraction cannot exist. To find a range of definition of such fraction, it is necessary to equate all denominator to zero. Having solved the received equation, you will find those values of a variable which need to be excluded from a range of definition.
2. If there is a root of even degree, it is obvious that the radicand can be only positive number. Further, we solve inequality in which the radicand is less than zero. We exclude the received values from a range of definition of our function.
3. If there is a logarithm. A logarithm range of definition all numbers which it is more than zero. I.e. to find the values of a variable which are not entering a range of definition it is necessary to make and solve inequality in which expression under a logarithm is less than zero.
4. If in function there are inverse trigonometrical functions, such as arcsine and arccosine. They are defined, only on an interval [-1;1]. Therefore, it is necessary to check at what values of a variable the expression standing under these functions gets to this interval.
5. Can be present at function at once a little from the listed options, in this case it is necessary to consider them all and the combination from all results will be a range of definition of function.