# Is domain the independent or dependent variable?

Feb 2, 2015

None of the two, actually. However, the domain is related to the independent variable, as it is the set of all the "permitted" values for the independent variable to assume. In particular, given a function, you must be sure that:

1. If there is a fraction, the denominator can't be zero;
2. If there is an even root, its argument must be positive or zero;
3. If there is a logarithm, its argument must be strictly positive.

These requests can of course be combined, as for example in $\setminus \sqrt{\setminus \log \left(\setminus \frac{x}{x + 1}\right)}$.

Once you find out which values of $x$ are permitted for the expression to have sense, you take the set of all those values, and obtain the domain of the function.