Answer:
D
Step-by-step explanation:
The domain must not let 1/3 x + 2 go less than 0. So equate this binomial to 0 and then use the < or > symbol to indicate what the minimum value is.
1/3 x + 2 = 0 Subtract 2 from both sides
1/3 x = - 2 Multiply 3
3(1/3) x = - 2 * 3
x = - 6
So if x is less than - 6 the binomial will go negative and that is not a permitted value at this level.
So x must be - 6 or bigger.
Let's see what happens when x = - 6
1/3 ( - 6) + 2
-2 + 2
0
That's the minimum value for the domain.
Now try - 9
1/3(-9) + 2
- 3 + 2 = -1
That means you will have √-1 which does not exist in the rational world.
Now try x = 9
1/3 (9) + 2
3 + 2 = 5 which is fine.
So the answer you seek is x ≥ -6
