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2007 AMC 12B Problems/Problem 9: Difference between revisions

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New page: 3x-1 =5 x= 2 4+2+1=7
 
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3x-1 =5
A function <math>f</math> has the property that <math>f(3x-1)=x^2+x+1</math> for all real numbers <math>x</math>.  What is <math>f(5)</math>?
x= 2
 
4+2+1=7
<math>(A)7</math> <math>(B)13</math> <math>(C)31</math> <math>(D)111</math> <math>(E)211</math>
 
== Solution ==
 
<math>3x-1 =5 \implies x= 2</math>
<math>f(3(2)-1) = 2^2+2+1=7 \implies (A)</math>

Revision as of 20:46, 2 July 2008

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

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

Solution

$3x-1 =5 \implies x= 2$ $f(3(2)-1) = 2^2+2+1=7 \implies (A)$

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