SOLUTION: Given that {{{ l(x)= 2sqrt (x)-5 }}} and {{{ m(x)= sqrt (x)-4 }}}, determine the following combinations of functions in the simplest form and fill in the blank spaces by stating th

Question 951103: Given that and , determine the following combinations of functions in the simplest form and fill in the blank spaces by stating the combined function's domain and range.

Very confused on what to do for this question. Would it just be:

How would you find the Domain and Range from that?
Thank you,
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Domain is dictated by values that are not allowed.
So look at the denominator first.
The denominator cannot equal zero so,

So is excluded from the domain.
Also in the denominator, the argument for the square root must be non-negative so,
.
Now look at the numerator, it has the same square root restriction as the denominator.
So then putting it all together.
Domain:[,)U(,)
.
.
.
For the range, look at the limit values from the domain,
When , .
As x increases towards 16, y decreases towards .
When you approach 16 from the right, y increases towards .
When x approaches infinity, y approaches 2.
So then putting this all together,
Range : (,)U(,)
.
.
.

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