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2007 AMC 12B Problem 9

Problem 9 of 25EasierAlgebra

A function ff has the property that f(3x−1)=x2+x+1f(3x-1)=x^2+x+1 for all real numbers x.x. What is f(5)?f(5)?

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Solution

Setting 3x−1=53x-1=5 gives x=2.x=2. Then f(5)=22+2+1=7. f(5)=2^2+2+1=7. Thus, the correct answer is A.

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Concepts: function · substitution

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.