 # How to find a function range of definition

Before carrying out some transformations of the equation of function, it is necessary to find a function range of definition as during transformations and simplifications information on permissible values of an argument can be lost.

## Instruction

1. If in the equation of function there is no denominator, then all real numbers from minus infinity to plus infinity will be its range of definition. For example, y = x + 3, its range of definition is all numerical straight line.

2. The case when in the equation of function there is a denominator is more difficult. As division into zero gives uncertainty of value of function, function arguments which involve such division, exclude from a range of definition. They say that in these points functionof not defined. To define such values x, it is necessary to equate a denominator to zero and to solve the turned-out equation. Then the range of definition of function will possess all values of an argument, except those that nullify a denominator. Let's consider a simple case: y = 2/(x-3). It is obvious that at x = 3, the denominator is equal to zero, so we cannot define y. A range of definition of this function, x - any number, except 3.

3. Sometimes the denominator contains expression which addresses in zero in several points. Periodic trigonometrical functions are that, for example. For example, y = 1/sin x. The denominator of sin x addresses in zero at x = 0, π,-π, 2π,-2π, etc. Thus, y range of definition = 1/sin x, are all x, except x = 2πn where n are all integers.

Author: «MirrorInfo» Dream Team