求值域 f(x)=x+3/x-1 x∈[3,4]
问题描述：
求值域 f(x)=x+3/x-1 x∈[3,4]
答
f(x)=(x+3)/(x-1)=(x-1+4)/(x-1)=1+4/(x-1),当x∈[3,4]时,f(x)随x增加而递减,f(x)max=f(3)=3,f(x)min=f(4)=7/3,值域为f(x)∈[7/3,3]
求值域 f(x)=x+3/x-1 x∈[3,4]
f(x)=(x+3)/(x-1)=(x-1+4)/(x-1)=1+4/(x-1),当x∈[3,4]时,f(x)随x增加而递减,f(x)max=f(3)=3,f(x)min=f(4)=7/3,值域为f(x)∈[7/3,3]