AoPSWiki
Our Precalculus course starts on Dec. 4. Master trig, complex numbers, and vectors and matrices in 2 and 3 dimensions. Click here to enroll today!
Personal tools

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
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.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us