Difference between revisions of "1998 AHSME Problems/Problem 17"
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Clarkculus (talk | contribs) (Undo revision 217553 by Gaurishasagar (talk)) (Tag: Undo) |
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: (b) <math>f(0) = 2</math>. | : (b) <math>f(0) = 2</math>. | ||
| − | What is the value of <math>f( | + | What is the value of <math>f(1998)</math>? |
<math>\mathrm{(A)}\ 0 | <math>\mathrm{(A)}\ 0 | ||
| Line 10: | Line 10: | ||
\qquad\mathrm{(C)}\ 1996 | \qquad\mathrm{(C)}\ 1996 | ||
\qquad\mathrm{(D)}\ 1998 | \qquad\mathrm{(D)}\ 1998 | ||
| − | \qquad\mathrm{(E)}\ 2000</math> | + | \qquad\mathrm{(E)}\ 2000</math> |
| − | |||
== Solution == | == Solution == | ||
<cmath>f(1998 + 0) = 1998 + f(0) = 2000 \Rightarrow \mathrm{(E)}</cmath> | <cmath>f(1998 + 0) = 1998 + f(0) = 2000 \Rightarrow \mathrm{(E)}</cmath> | ||
Latest revision as of 21:16, 28 March 2024
Problem
Let 
be a function with the two properties:
- (a) for any two real numbers
and 
, 
, and - (b)
.
and 
, 
, and
.What is the value of 
?
Solution
![\[f(1998 + 0) = 1998 + f(0) = 2000 \Rightarrow \mathrm{(E)}\]](http://latex.artofproblemsolving.com/5/d/6/5d6457cf917203b3385c143415523c45f121254a.png)
The function 
satisfies these properties.
See also
| 1998 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
