If f(x+1) = 3x^2 + 6x + 3, then f(x) =

A)3x
B)3x+3
C)3x^2
D)3x^2 + 3
E) 3x^2 + 6x + 2

I like this question–it’s from the CB’s Subject Test book, right? I think I remember seeing it there.

Anyway, I think the easiest way to go is to backsolve: put (x + 1) in for x in each answer choice and see which one yields the desired result. You should see pretty quickly that (A) and (B) won’t work: they won’t give you an term. Try (C), though:

Yep—that worked! (C) is the answer.