2012-04-05 09:00:45

If f(4) = 23 and f(-1) = 3, which of the following could be f(x)?

(A) 5x + 3
(B) x² + x + 3
(C) 5x² - 2
(D) x² - x - 3
(E) x³ + 4

The correct answer is B

Explanation: The best approach to this question is to use the given x-values in each equation and see if the equation produces the correct outputs for the given inputs.

(A) f(x) = 5x + 3: 5(4) + 3 = 23, but 5(-1) + 3 = -2, so A only works for f(4).
(B) f(x) = x² + x + 3: (4)²+ (4) + 3 = 23, and (-1)² + (-1) + 3 = 3, so this works for f(4) and f(-1).
(C) f(x) = 5x² -2: 5(4)² - 2 = 78, but 5(-1)² -2 = 3, so this works for f(-1) only.
(D) f(x) = x² - x - 3: (4)² - 4 - 3 = 9, but (-1)² - (-1) - 3 = -1, so this works for neither f(4) nor f(-1).
(E) f(x) = x³ + 4: (4)³ + 4 = 68, but (-1)³ +4 = 3, so this works for f(-1) only.

Because only choice B’s function works for both f(4) and f(-1), choice B is correct.