Find the Domain

Problem

g(t)=√(,3−t)−√(,2+t)

Solution

1. Identify the constraints for the square root functions, which require the radicands (the expressions inside the square roots) to be greater than or equal to zero.

2. Set up the first inequality for the term √(,3−t)

3−t≥0

3. Solve the first inequality for t

−t≥−3

t≤3

4. Set up the second inequality for the term √(,2+t)

2+t≥0

5. Solve the second inequality for t

t≥−2

6. Find the intersection of the two solution sets to satisfy both conditions simultaneously:

−2≤t≤3

Final Answer

Domain: *[−2,3]

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