Question

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)

Answer 1

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(-1) + f(x2) ===> f(-x2) = f(x2);===> f(x)是偶函数

3) f(4*4) = f(4) + f(4) = 2

f(4*4*4) = f(4*4)+f(4)=2+1=3

所以 f(64) = 3 ,f(x)是偶函数,所以,f(-64) = 3

f(3x+1)+f(2x-6) = f( (3x + 1)(2x - 6))