2007 AMC 12B Problems/Problem 9

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Problem

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

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

Solution

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

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

See Also

2007 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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