函数f(x)对任意正实数x1,x2满足f(x1x2)=f(x1)+f(x2),已知f(8)=3,求f(√2)_数学解答

函数f(x)对任意正实数x1,x2满足f(x1x2)=f(x1)+f(x2),已知f(8)=3,求f(√2)

人气：497 ℃　时间：2019-08-18 22:16:43

解答

f(x1x2)=f(x1)+f(x2),令x1=x2=√2可得：f(2)= f(√2)+ f(√2)=2 f(√2).令x1=x2=2可得：f(4)= f(2)+ f(2)=2 f(2).令x1=2,x2=4可得：f(8)= f(2)+ f(4),因为f(4)= =2 f(2)所以f(8)= 3f(2)因为f(2)= 2 f(√2). 所以f(8)...