Difference between revisions of "2007 AMC 12B Problems/Problem 9"

Revision as of 21:47, 2 July 2008

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

$(A)7$ $(B)13$ $(C)31$ $(D)111$ $(E)211$

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

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

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	<math>3x-1 =5 \implies x= 2</math>		<math>3x-1 =5 \implies x= 2</math>
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	<math>f(3(2)-1) = 2^2+2+1=7 \implies (A)</math>		<math>f(3(2)-1) = 2^2+2+1=7 \implies (A)</math>