AoPSWiki
Do you have what it takes to be the next brilliant trader, researcher, or developer at Jane Street Capital? Find out in the Careers in Mathematics Forum.

1998 AHSME Problems/Problem 17

From AoPSWiki

Problem

Let f(x) be a function with the two properties:

(a) for any two real numbers x and y, f(x+y) = x + f(y), and
(b) f(0) = 2.

What is the value of f(1998)?

\mathrm{(A)}\ 0 \qquad\mathrm{(B)}\ 2 \qquad\mathrm{(C)}\ 1996\qquad\mathrm{(D)}\ 1998 \qquad\mathrm{(E)}\ 2000

Solution

f(1998 + 0) = 1998 + f(0) = 2000 \Rightarrow \mathrm{(E)}

The function f(x) = x+2 satisfies these properties.

See also

1998 AHSME (Problems)
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
Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us