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

Latest revision as of 00:01, 19 October 2020

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

$\mathrm{(A)}\ 7 \qquad \mathrm{(B)}\ 13 \qquad \mathrm{(C)}\ 31 \qquad \mathrm{(D)}\ 111 \qquad \mathrm{(E)}\ 211$

$3x-1 =5 \implies x= 2$

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

2007 AMC 12B (Problems • Answer Key • 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
All AMC 12 Problems and Solutions

@@ Line 1: / Line 1: @@
-x-1 =5
+== Problem ==
-x= 2
+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>?
-+2+1=7
+<math>\mathrm{(A)}\ 7 \qquad \mathrm{(B)}\ 13 \qquad \mathrm{(C)}\ 31 \qquad \mathrm{(D)}\ 111 \qquad \mathrm{(E)}\ 211</math>
+== Solution ==
+<math>3x-1 =5 \implies x= 2</math>
+<math>f(3(2)-1) = 2^2+2+1=7 \implies (A)</math>
+== See Also ==
+{{AMC12 box|year=2007|ab=B|num-b=8|num-a=10}}
+{{MAA Notice}}