Question 986589
The domain must be the set of numbers for which f(x) is defined.  There are two irrational expressions, each with its own acceptable domain.


{{{sqrt(x+18)}}} must have {{{x>=-18}}}.


{{{sqrt(x-10)}}}  must have x-10>=0 or  {{{x>=10}}}.


Look at these two requirements together to be sure both conditions will be satisfied for f(x).  Values for x between  -18 and +10 are still NOT allowed because those will not satisfy both of the separate domains.  Values of x must satisfy BOTH radical terms or expressions.  The domain for f(x) must be  {{{highlight(highlight(x>=10))}}}.  


The {{{-3}}} is important; it is a factor on one of the expressions.  It has no affect on the expression inside the square root function; it only affects the square root function AFTER x has been applied.  Unclear what you are confused on about the {{{-3}}}.  Subtraction of an expression instead of addition of an expression.  For real numbers, {{{sqrt(anything)}}}  must be either positive or zero.  If you want it to be negative, then it needs to be stated as negative, like  {{{-sqrt(anything)}}}.