2014-11-19 09:00:07
If f(3) = 21 and f(7) = 329, what is one possible value of f(x)?
(A) x3 - 2x
(B) 2x3 - 3x
(C) 2x2 + 3
(D) 3x2 - 2x
(E) x3 + 2x
The correct answer is A
Explanation: Simply plug in the two pairs of inputs and outputs into the possible functions to see which one works: Start with f(3) = 21:
(A) x3 - 2x = 33 - 2(3) = 21. Works.
(B) 2x3 - 3x = 2(3)3 - 3(3) = 45. Does not work.
(C) 2x2 + 3 = 2(3)2 + 3 = 21. Works.
(D) 3x2 + 2x = 3(3)2 - 2(3) = 21. Works.
(E) x3 + 2x = (3)3 + 2(3) = 33. Does not work.
Now, try just the ones that worked for f(3) for f(7):
(A) x3 - 2x = 73 - 2(7) = 329. Works.
(C) 2x2 + 3 = 2(7)2 + 3 = 101. Does not work.
(D) 3x2 + 2x = 3(7)2 - 2(7) = 133. Does not work.
Choice A is the only one that provides a function that works for both sets of input and output.