Final answer:
The domain of the expression sqrt(8-12a) is a <= 2/3.
Step-by-step explanation:
The domain of the given expression, sqrt(8-12a), represents the set of values that the variable a can take without causing any issues in the expression.
In this case, the square root function requires the argument inside the square root to be non-negative, since imaginary numbers are not considered in this context.
Therefore, we need to find the values of a that make 8-12a non-negative.
To ensure that the expression inside the square root is non-negative, we set 8-12a >= 0 and solve for a.
Starting with 8-12a >= 0, we subtract 8 from both sides and then divide by -12 to isolate a.
This yields a <= 2/3.
Therefore, the domain of the expression sqrt(8-12a) is a <= 2/3.