Question

已知f(x)在定义域x>0上为增函数,满足f(xy)=f(x)+f(y),且f(2)=1

Answer 1

(1)

因为f(xy)=f(x)+f(y),f(2)=1

f(4)=f(2*2)=2f(2)=2

f(8)=f(2*4)=f(2)+f(4)=1+2=3

(2)

因为f(x)在定义域x>0上为增函数,f(xy)=f(x)+f(y)

所以f(x)+f(x-2)=f(x(x-2))