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)?
Answer Choices:
A. 0
B. 2
C. 1996
D. 1998
E. 2000
Solution:
Note that f(x)=f(x+0)=x+f(0)=x+2 for any real number x. Hence f(1998)=2000. The function defined by f(x)=x+2 has both properties: f(0)=2 and f(x+y)=x+y+2=x+(y+2)=x+f(y).
OR
Note that
2=f(0)=f(−1998+1998)=−1998+f(1998).
Hence f(1998)=2000.