Understand a set of all values of a variable at which function makes sense as length of function or the field of its definition. Determination of length of function means search of such sizes.
It is required to you
- - mathematical reference book.
Instruction
1. Consider function regarding presence at it of specific members – fractions, a root, a logarithm, etc. Each of such elements will suggest you an idea where it is necessary to look for a function range of definition and in what part it can be excluded.
2. If at expression of function there is a fraction, then its denominator should not be equal to zero, it is impossible to divide into zero. In this case equate a denominator from a variable to this size then exclude values of a variable at which function does not make sense.
3. If in expression of function there is a root of even degree, then exclude negative numbers from the field of its definition.
4. If at expression of function there is a logarithm, then the field of its definition has to be more than zero. To exclude from values of a variable at which function does not make sense solve inequality in which expression under a logarithm will be less than zero.
5. Define other conditions under which function does not make sense. Proceeding from it, make equality or inequality where at the left part there will be a variable, and in right a condition of expediency of function. Solve it, and you receive values of function which should be excluded.
6. Make a function range of definition taking into account the excluded values.