SOLUTION: find the domain for h(x)= square root of (13+x)

Question 1077352: find the domain for h(x)= square root of (13+x)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The stuff under the square root (known as the radicand) cannot be negative. So that means that the "13+x" must be 0 or a positive value.

Forcing 13+x to be 0 or positive means . Subtract 13 from both sides and we'll end up with

Saying is the same as saying "x can be any number as long as it's -13 or larger". This forms what is known as the domain. The domain is the set of allowed input x values of a function. It's a rule to make sure that no errors occur. If we plug x = -14, which is NOT -13 or larger, then we run into issues of taking the square root of a negative number.

So the domain is the set of all real numbers x such that

Your teacher may want you to write this in interval notation. If so, then you would write [-13, infinity) where you replace "infinity" with the infinity symbol if needed. Notice how I placed a square bracket next to -13. This tells the reader "include -13 in the interval". The curved parenthesis means "exclude the endpoint from the interval".

Note: infinity or -infinity cannot be included because it's not a number. It's impossible to get to infinity. This is why infinity and -infinity will have curved parenthesis. This is a rule you should memorize.
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