设f(x)=5x/(x-3),且f[g(x)]=4-x求g(x)_数学解答

设f(x)=5x/(x-3),且f[g(x)]=4-x求g(x)

人气：402 ℃　时间：2020-06-24 16:53:32

解答

f(x)=(5x-15+15)/(x-3)=[5(x-3)+15]/(x-3)=5+15/(x-3)=4-[-1-15/(x-3)]令x=g(x)f[g(x)]=4-x=4-[-1-15/(g(x)-3)]=4-x-1-15/(g(x)-3)=x15/[g(x)-3]=-x-1g(x)=(3x-12)/(x+1)