DOMAIN ANALYSIS

Informal Explanations:

All real values of 'x' - infinity to  + infinity that permits a function to exist.

There are only 3 types functions that restrict domains.

1.Functions under a even root radical, or exponent m/n has n only as even  number.
(ex x^1/2; x^3/4;x^5/4--) have to be >=0

domain restriction graph of fractional exponents
you can experiment in the above link apart from study.

2.Functions that have denominators whose 'x' value will make it '0'.
The function is DNE at the 'x' value.(ex 3x-1/3x-2  cannot have x=2/3  f(2/3) is DNE)
Domain of rational functions

3.log f(x) must have f(x) greater than'0'.
 The term of the log ;That is f(x) must be >0.
Ex: log{ (x^3)-7} must be such x^3-7 >0 (be careful to exclude '0')

It is the same rule for all types of bases.Bear in mind that, Base 0 does exist as it is absurd.