Given y=6-[sqrt(4-3x)], focus on the sqrt function: sqrt(4-3x). Since the input of this function cannot be negative, any x-value used must pass the test 4-3x>0. This is equivalent to 4>3x, or 3x<4, or x < 4/3. This eliminates choice E.
Second, if the y value is an integer, then sqrt(4-3x) must be an integer.
Checking answers A through D:
A: sqrt(4-3) = sqrt(1) = 1 (OK) Then y=6-[sqrt(1)] = 5 (NO)
B: sqrt(4-0) = 2 (OK) Then y=6-2 = 4 (NO)
C: sqrt(4-0) = 2 (OK) Then y=6-2 = 4 (NO)
D: sqrt(4-15) Not OK; eliminate
Correct answer: F: None of the above answers are correct
