f(1/2)+f(1/2)=f(1/4) =2
當且僅當x屬於M,且M是正實數的真子集時,函數值f(x)的集合為0<=x<=2
所以1/4屬於M
f(1/4)+f(1/2)=f(1/8) =3
x=3不屬於0<=x<=2
所以1/8不屬於M
(2)令f(x)的反函數即f(-1)(x)=g(x)
f(X1)+f(X2)=f(X1*X2)
則g(f(X1)+f(X2))=X1*X2
令f(X1)=y1,f(X2)=y2
則g(y1+y2)=g(y1)*g(y2)
即f(-1)(X1+X2)=f(-1)(X1)* f(-1)(X2)
(3)R上遞減的函數f(x),其反函數g也遞減
g(X^2+X)*g(X+2)=g(x^2+2x+2) <=1/4=1/2+1/2=g(f(1/2)+f(1/2))=g(1+1)=g(2)
所以x^2+2x+2>=2
解得x>=0或x<=-2又0<=x<=2
得0<=x<=2