函数f(x)的定义域为D=﹛x/x≠0﹜且满足对于任意x1,x2∈0,有f(x1乘x2)=f(x1)+f(x2)⑴.求f(1)值⑵判断f(x)的奇偶性⑶如果f(4)=1,f(3x+1)+f(2x-6)≤3且f(x)在(0,+∞)上是增函数,求x的取值范围
问题描述:
函数f(x)的定义域为D=﹛x/x≠0﹜且满足对于任意x1,x2∈0,有f(x1乘x2)=f(x1)+f(x2)
⑴.求f(1)值
⑵判断f(x)的奇偶性
⑶如果f(4)=1,f(3x+1)+f(2x-6)≤3且f(x)在(0,+∞)上是增函数,求x的取值范围
答
1) 令x1 = x2 = 1;带入f(x1x2)=f(x1)+f(x2);f(1) = f(1) + f(1) ===> f(1) = 0;2) 令x1 = x2 = -1;带入f(x1x2)=f(x1)+f(x2);0 = f(1) = f(-1) + f(-1) ===> f(-1) = 0;令x1 = -1;带入f(x1x2)=f(x1)+f(x2);f(-x2) = f...