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

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==Problem==
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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>?
  
<math>(A)7</math> <math>(B)13</math> <math>(C)31</math> <math>(D)111</math> <math>(E)211</math>
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<math>\mathrm{(A)}\ 7 \qquad \mathrm{(B)}\ 13 \qquad \mathrm{(C)}\ 31 \qquad \mathrm{(D)}\ 111 \qquad \mathrm{(E)}\ 211</math>
  
 
== Solution ==
 
== Solution ==
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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>
  
==See Also==
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== See Also ==
 
{{AMC12 box|year=2007|ab=B|num-b=8|num-a=10}}
 
{{AMC12 box|year=2007|ab=B|num-b=8|num-a=10}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 00:01, 19 October 2020

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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