# What is the domain and range of # c(x) =1/( x^2 -1) #?

The domain is

Therefore,

The real solutions are when the discriminant is

The solutions to this equation is obtained with a sign chart.

graph{1/(x^2-1) [-7.02, 7.024, -3.51, 3.51]}

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Domain: (x \in (-\infty, -1) \cup (-1, 1) \cup (1, \infty))

Range: (c(x) \in (-\infty, -\infty) \cup (-\infty, -1) \cup (-1, 0) \cup (0, \infty) \cup (\infty, \infty))

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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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