Find the Domain

Problem

ƒ(a)=(2*a+3)3−√(,8*a+12)−√(,18*a+27)

Solution

1. Identify the constraints for the expression. The polynomial term (2*a+3)3 is defined for all real numbers, but the square root terms require their radicands to be non-negative.

2. Set up the inequalities for the square root functions.

8*a+12≥0

18*a+27≥0

3. Solve the first inequality for a

8*a≥−12

a≥−12/8

a≥−3/2

4. Solve the second inequality for a

18*a≥−27

a≥−27/18

a≥−3/2

5. Determine the intersection of the constraints. Since both inequalities result in a≥−3/2 the domain is the set of all values satisfying this condition.

Final Answer

Domain:a≥−3/2

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