2007 AMC 12B Problem 9 — Solution | LIVE by Po-Shen Loh

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2007 AMC 12B Problem 9

Attempt Problem 9 of the 2007 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

9.

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

$7$

$13$

$31$

$111$

$211$

Answer: A

Concepts:function substitution

Difficulty rating: 1200

Solution:

Setting $3x-1=5$ gives $x=2.$

Then $f(5)=2^2+2+1=7.$

Thus, the correct answer is A.

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