How to find a function range of definition

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.


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