Difference between revisions of "2002 AMC 10P Problems/Problem 11"
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| + | == Problem 12 == | ||
| + | |||
| + | For <math>f_n(x)=x^n</math> and <math>a \neq 1</math> consider | ||
| + | |||
| + | <math>\text{I. } (f_{11}(a)f_{13}(a))^{14}</math> | ||
| + | |||
| + | <math>\text{II. } f_{11}(a)f_{13}(a)f_{14}(a)</math> | ||
| + | |||
| + | <math>\text{III. } (f_{11}(f_{13}(a)))^{14}</math> | ||
| + | |||
| + | <math>\text{IV. } f_{11}(f_{13}(f_{14}(a)))</math> | ||
| + | |||
| + | Which of these equal <math>f_{2002}(a)?</math> | ||
| + | |||
| + | <math> | ||
| + | \text{(A) I and II only} | ||
| + | \qquad | ||
| + | \text{(B) II and III only} | ||
| + | \qquad | ||
| + | \text{(C) III and IV only} | ||
| + | \qquad | ||
| + | \text{(D) II, III, and IV only} | ||
| + | \qquad | ||
| + | \text{(E) all of them} | ||
| + | </math> | ||
| + | |||
== Solution 1== | == Solution 1== | ||
Revision as of 17:43, 14 July 2024
Problem 12
For 
and 
consider
Which of these equal 
Solution 1
See also
| 2002 AMC 10P (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
