The topic of "seeking monotonic increase in mathematics in senior one"

Solution: f(0+0)=f(0)+f(0)- 1, so f(0)= 1.

F (x)+f (-x)-1= f (x+(-x)) = f (0) =1,so f(-x)=2-f(x).

So f(- 1/2)=2-2=0.

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

So when x>0, x-1/2 >; -1/2, when f(x- 1/2)>0, so

When x>0, f (x)-1>; 0

Let x1> X2, then f (x1) = f (x1-x2+x2) = f (x1-x2)+f (x2)-1= f (x2)+f (x/kloc-.

Because x1-x2 >; 0, so f (x1-x2)-1>; 0, so f(x 1)>F(x2), so the function is increasing function.