Question

设函数y=f(x)的定义域为(0,+∝)且f(xy)=f(x)+f(y),f(8)=3则f(根号2)等于

Answer 1

f(xy)=f(x)+f(y),
所以
f(2*2)=f(2)+f(2)
即f(4)=2f(2)
f(2)=f(√2)+f(√2)=2f(√2)
f(8)=f(2)+f(4)=3f(2)=3*2f(√2)=6f(√2)
从而
f(√2)=f(8)/6=3/6=1/2.