If log42fx1-fx=x then f2010+f-2009 is equal to
0
-1
1
2
log42fx1-fx=x⇒2fx1-fx=4x 1Replacing x by 1-x, we get 2f1-x1-f1-x=41-x 2
Multiplying (1) and (2), we get
2fx1-fx2f1-x1-f1-x=41-x⇒fxf1-x=1-fx-f1-x+fxf1-x⇒fx+f1-x=1Putting x=2010, we getf2010+f-2009=1