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 $f(1998)$ ?

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

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

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