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Answer:
3x - 6
Step-by-step explanation:
To evaluate f(2x) and f(x + 2) substitute x = 2x and x = x + 2 into f(x)
f(2x) = 3(2x) - 2 = 6x - 2
f(x + 2) = 3(x + 2) - 2 = 3x + 6 - 2 = 3x + 4
Thus
f(2x) - f(x + 2)
= 6x - 2 - (3x + 4)
= 6x - 2 - 3x - 4
= 3x - 6
Candidates range from 1 to 50.
50/4=12 positive integers are multiples of 4
50/6=8 positive integers are multiples of 6
50/12=4 positive integers are multiples of 12 (LCM of 4 and 6)
By the inclusion/exclusion principle, the number of multiples of either 4 or 6 is equal to 12+8-4=16.
Therefore, the complement is the number of positive integers that are multiples of neither 4 nor 6 = 50-16=34.