Difference between revisions of "2007 AMC 12B Problems/Problem 9"
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| + | == Problem == | ||
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>? | 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>? | ||
| − | <math>(A)7 | + | <math>\mathrm{(A)}\ 7 \qquad \mathrm{(B)}\ 13 \qquad \mathrm{(C)}\ 31 \qquad \mathrm{(D)}\ 111 \qquad \mathrm{(E)}\ 211</math> |
== Solution == | == Solution == | ||
| + | <math>3x-1 =5 \implies x= 2</math> | ||
| − | |||
<math>f(3(2)-1) = 2^2+2+1=7 \implies (A)</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}} | ||
Latest revision as of 00:01, 19 October 2020
Problem
A function 
has the property that 
for all real numbers 
. What is 
?
Solution
See Also
| 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 | |
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