Answer:
The given function is:
f(x) = 2/(9x+8)
The denominator cannot be equal to zero, since division by zero is undefined. Therefore, we need to solve the inequality:
9x+8 ≠ 0
Solving for x, we get:
x ≠ -8/9
Therefore, the domain of the function is all real numbers except -8/9. We can express this in interval notation as:
(-∞, -8/9) U (-8/9, ∞)