Question

f(x+y)=f(x)+f(y)-1,f(-1/2)=0.求单调性

Answer 1

f(-1/2)=f(-1/2+0)

=f(-1/2)+f(0)-1

=f(0)-1=0

f(0)=1

f(-1)=f(-1/2)+f(-1/2)-1=-1

f(-2)=f(-1)+f(-1)-1=-1-1-1=-3

所以函数在(-∞,0]内单调递减