高一函数题:若非零函数f(x)对任意实数a,b均有f(a+b)=f(a)乘f(b),且当x1; 求证:f(x)>0
问题描述:
高一函数题:若非零函数f(x)对任意实数a,b均有f(a+b)=f(a)乘f(b),且当x1; 求证:f(x)>0
高一函数题:若非零函数f(x)对任意实数a,b均有f(a+b)=f(a)乘f(b),且当x1;
求证:f(x)>0
答
f(a+b) = f(a)f(b)put a=b=0f(0) = f(0)f(0)=> f(0) = 1case 1: for x 1 >0 (true)case 2: x=0f(0) =1 >0 (true)case 3: for x>0-xf(x) > 0 ( f(-x) >0 , f(0) =1 )