What is the domain of #sqrt(x^2-9)#?

1 Answer
Oct 11, 2016

The domain of this expression is #{x|x < -3# or #x > 3}#.

Explanation:

To find restrictions to the domain of a square root expression, you must determine which values of the variable will make the radicand have a negative value.

#x^2 - 9 < 0#
#x^2 - 9 + 9 < 0 + 9#
#x^2 < 9#
#sqrtx^2 < sqrt9#
#x < +-3#

This actually tells us that #x# cannot be between #-3# and #3#, inclusive. Therefore #x# must be less than #-3# or greater than #3#.