设定义R上的运算:a*b=ab+2a+b,则函数f(x)=(1/3)^[x*(x-1)]的最大值是
问题描述：
设定义R上的运算:a*b=ab+2a+b,则函数f(x)=(1/3)^[x*(x-1)]的最大值是
答
解由a*b=ab+2a+b知[x*(x-1)]=x(x-1)+2x+x-1=x^2+2x-1=(x+1)^2-2≥-2即[x*(x-1)]≥-2即0＜(1/3)^[x*(x-1)]≤(1/3)^(-2)即0＜f(x)≤1/[(1/3)^(2)]即0＜f(x)≤9故函数f(x)=(1/3)^[x*(x-1)]的最大值是9....