 # How to find a range of definition of function of the decision

Range of definition of function is the set of values of an argument at which this function exists. Allocate various ways of finding of a range of definition of function.

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## Instruction

1. Consider a range of definition of some elementary functions. If function has an appearance at = and / in, then its range of definition are all values in, except zero. At the same time the number and is any number. For example, to find a function range of definition at = 3/2kh-1, it is necessary to find those values x for which the denominator of this fraction is not equal to zero. That to make it, find values x at which the denominator is equal to zero. For this purpose equate a denominator to zero and find value, having solved the turned-out equation: х: the 2nd – 1 = 0; the 2nd = 1; x = ½; x = 0.5. From this it follows that a range of definition of function will be any number, except 0.5.

2. To find a range of definition of function of a radicand with an even indicator, consider the fact that this expression has to be more or equally to zero. For example: Find a function range of definition at = 3kh-9. Referring to the above-stated condition, expression will take inequality form: the 3rd – 9 ≥ 0. Solve it as follows: the 3rd ≥ 9; x ≥ 3. Means, all values x which it is more will be a range of definition of this function or are equal 3, i.e. x ≥ 3.

3. Finding a range of definition of function of a radicand with an odd indicator, it is necessary to remember the rule that x – can be any number if the radicand is not fraction. For example, to find a function range of definition at =³ √ 2kh-5, it is enough to specify that x - any real number.

4. When finding a range of definition of logarithmic function, you remember that the expression standing under the sign of a logarithm has to be positive size. For example, find a function range of definition at = log2 (the 4th – 1). Considering the above condition, you find a function range of definition as follows: the 4th – 1> 0; from here the 4th> 1; x> 0.25. Thus, a function range of definition at = log2 (the 4th – 1) will be all values x> 0.25.

Author: «MirrorInfo» Dream Team