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

Answer 1

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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Answer 2

[ \text{Domain: } x \in \mathbb{R}, x \neq 1 ] [ \text{Range: } f(x) \in \mathbb{R}, f(x) \neq 0 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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