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2000 AMC 12 Question 15

AMC12 · 2000 AMC 12

Question 15

Let $f$ be a function for which $f\!\left(\dfrac{x}{3}\right) = x^2 + x + 1.$ Find the sum of all values of $z$ for which $f(3z) = 7.$
  1. $-\dfrac{1}{3}$
  2. $-\dfrac{1}{9}$
  3. $0$
  4. $\dfrac{5}{9}$
  5. $\dfrac{5}{3}$