2007 AMC 12B Problems/Problem 9

Problem

A function $f$ has the property that $f(3x-1)=x^2+x+1$ for all real numbers $x$ . What is $f(5)$ ?

$\mathrm{(A)}\ 7 \qquad \mathrm{(B)}\ 13 \qquad \mathrm{(C)}\ 31 \qquad \mathrm{(D)}\ 111 \qquad \mathrm{(E)}\ 211$

$3x-1 =5 \implies x= 2$

$f(3(2)-1) = 2^2+2+1=7 \implies (A)$

2007 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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