2

Part of 2012 CHMMC Fall

Problems(2)

2012 Fall Team #2

Source:

Consider a triangle

ABC

D

AB

E

BE = 1

F

be the intersection of

AE

CD

AD = 1

DB = 2

BE = 1

EC = 3

CA = 5

. Find the value of the area of

ECF

minus the area of

ADF

2012 Fall CHMMC Tiebreaker 2 continuous f(x + f(y)) = f(x + y) + y

Source:

Find all continuous functions

f : R \to R

f(x + f(y)) = f(x + y) + y,

x, y \in R

. No proof is required for this problem.

algebraCHMMCfunctionalcontinuous function