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2007 AMC 12B Problems/Problem 9

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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 (Problems • Resources)
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

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2007_AMC_12B_Problems/Problem_9"

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