AMC12 2007 B

AMC12 2007 B · Q9

AMC12 2007 B · Q9. It mainly tests Functions basics, Manipulating equations.

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

函数 $f$ 满足对于所有实数 $x$，$f(3x-1)=x^2+x+1$。$f(5)$ 等于多少？

(A) 7 7

(B) 13 13

(C) 31 31

(D) 111 111

(E) 211 211

Answer

Correct choice: (A)

正确答案：（A）

Solution

$3x-1 =5 \implies x= 2$ $f(3(2)-1) = 2^2+2+1=7 \implies (A)$

$3x-1 =5 \implies x= 2$ $f(3(2)-1) = 2^2+2+1=7 \implies (A)$

Topics

AL.010 Functions basics AL.016 Manipulating equations

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