f(x)=x+1/(1+x)=[(x+1)+1/(1+x)]-1根据均值不等式的知识有:[(x+1)+1/(1+x)]>=2*根号[(x+1)*1/(x+1)]=2故f(x)>=2-1=1当且仅当(x+1)=1/(x+1)时,即x=0或-2时,等号成立取x=0,这满足x>-1.这时f(x)取得最小值1.即f(x)的最...