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

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==Problem==
 
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>?
 
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>?
  
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== Solution ==
 
== Solution ==
 
 
<math>3x-1 =5 \implies x= 2</math>
 
<math>3x-1 =5 \implies x= 2</math>
  

Revision as of 23:56, 14 February 2019

Problem

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

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

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

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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