已知定义在R上恒不为0的函数y=f(x),当x>0时,满足f(x)>1,且对于任意的实数x,y都有f(x+y)=f(x)f(y) (1)证明f(-x)=-f(x)/1 (2)证明f(x-y)=f(x)/f(y)

问题描述:

已知定义在R上恒不为0的函数y=f(x),当x>0时,满足f(x)>1,且对于任意的实数x,y都有f(x+y)=f(x)f(y) (1)证明f(-x)=-f(x)/1 (2)证明f(x-y)=f(x)/f(y)
(1)证明的是f(-x)=1/-f(x) 前面的打错了

令 y=0f(x+0) = f(x)*f(0)∴ f(0) = 1令 y = - xf(x-x) = f(x)*f(-x)f(0) = f(x)*f(-x) = 1∴ f(-x) = 1/ f(x) (你还是写错题目了)由(1)知f(-y) = 1/f(y)f(x-y) = f[x+(-y)] = f(x)*f(-y) = f(x) / f(y)...