Question

If f(n) = (2n + 3)2 – 2n, which statement is true?

1. f(3) = 75
2. f(2)= 619
3. f(5) = 16
4. f(-4)= -3

Answer 1

Upon evaluating the function f(n) = (2n + 3)2 – 2n at the given values, the true statement is f(3) = 75.

Step-by-step explanation:

To determine which statement about the function f(n) = (2n + 3)2 – 2n is true, we must evaluate the function at the given values of n.

1. For f(3), we calculate (2·3 + 3)2 – 2·3 = (6 + 3)2 – 6 = 92 – 6 = 81 – 6 = 75.
2. For f(2), we calculate (2·2 + 3)2 – 2·2 = (4 + 3)2 – 4 = 72 – 4 = 49 – 4 = 45, not 619.
3. For f(5), we calculate (2·5 + 3)2 – 2·5 = (10 + 3)2 – 10 = 132 – 10 = 169 – 10 = 159, not 16.
4. For f(-4), we calculate (2·(-4) + 3)2 – 2·(-4) = (-8 + 3)2 – (-8) = (-5)2 – (-8) = 25 + 8 = 33, not -3.

Therefore, the statement that is true is f(3) = 75.