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设f(x)=5x/(x-3),且f[g(x)]=4-x求g(x)
题目详情
设f(x)=5x/(x-3),且f[g(x)]=4-x求g(x)
▼优质解答
答案和解析
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)=x
15/[g(x)-3]=-x-1
g(x)=(3x-12)/(x+1)
=[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)=x
15/[g(x)-3]=-x-1
g(x)=(3x-12)/(x+1)
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