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1998 AHSME Problems/Problem 17

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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
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Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
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