SOLUTION: When finding the domain of: f(x) = sqrt(x+18) -3sqrt(x-10) I know that the domain of of x+18>=-18 but why is the 2nd part x=+10, my main question is what happens to -3 does it bec

Question 986589: When finding the domain of: f(x) = sqrt(x+18) -3sqrt(x-10)
I know that the domain of of x+18>=-18 but why is the 2nd part x=+10, my main question is what happens to -3 does it become irrelevant and if so why?
Also, the domain is x>=+10 why isn't it including -18? wouldn't something like x>=-18 and x>=+10 make more sense?
Thanks
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
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.

must have .

must have x-10>=0 or .

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 .

The 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 . Subtraction of an expression instead of addition of an expression. For real numbers, must be either positive or zero. If you want it to be negative, then it needs to be stated as negative, like .
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