1998 AHSME Problems/Problem 17

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 (ProblemsAnswer KeyResources)
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. AMC logo.png