函数Y=2x/(x-1)的值域是______.

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函数Y=2x/(x-1)的值域是______.
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函数Y=2x/(x-1)的值域是______.
函数Y=2x/(x-1)的值域是______.

函数Y=2x/(x-1)的值域是______.
y=2(x-1+1)/(x-1)
=2[(x-1)/(x-1)+1/(x-1)]
=2+2/(x-1)
2/(x-1)≠0
所以2+2/(x-1)≠2
值域(-∞,2)∪(2,+∞)

Y=2x/(x-1)
xy-y=2x
x=y/(y+2)
=1-1/(y+2)
y≠2
值域是y≠2的所有实数