How do you find the domain and range of #f(x) = 2/(x-1)#?

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Answer 1 · 2015-09-02T21:11:40

The domain is #color(red)(x≠1)#; the range is #color(red)(y≠0)#.

#f(x) = 2/(x-1)#

When #x=1, y=2/0#.

The value of #2/0# is undefined, so #x# cannot equal #1#.

The domain is #x≠1#.

As #x# becomes large and positive, the value of #y# approaches zero but never reaches it.

The same thing happens as #x# becomes large and negative.

#y# can have any value except zero.

The range is is #y≠0#.

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