domain with unknown characters

Question

In Algebra 1 I am given the following problem:

 

 

The domain of f(x) = √x + 3 is the set {?}.

 

(x + 3 is all under the same square root sign.)

Please help me.

Answer 1

Hi James.

 

The "stuff" under the radical can never be negative, so to be sure than it never gets negative, you can set all of the stuff under the radical to be at least 0 or more.

 

So if SqRt(x+3) is what you are given, then

 

Set x+3 ≥ 0

 

then subtract 3 from both sides and find that

 

x ≥ -3

 

And this is the domain, that x ≥ -3.