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.
It is required to you
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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.