1. In most texts the solution to a question such as square root x = -6 is
x is undefined.
Yet when teaching to solve
xsquared = 36
x = +6 or -6
There appears to be a contradiction here. My question is when, where and why do we use the principle square root, not both + and -? This often occurs as the extraneous root in the solution of radical equations and in stating the domain and range of functions involving square roots.
2. Are there any simple rules for determining whether equations are functions without graphing them and doing a vertical line test?