# Given the function #g(x)=(x^2-3x-4)/(x-5)#, how do you find the domain?

Since equating the denominator to zero and solving for x yields the value that x cannot be, the denominator of g(x) cannot be zero as this would render g(x) undefined.

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graph{[-74, 86, -36.8, 43.2]};x^2-3x-4)/(x-5)

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To find the domain of the function g(x) = (x^2 - 3x - 4) / (x - 5), you need to identify any values of x that would make the denominator zero, since division by zero is undefined. Set the denominator equal to zero and solve for x to find any restrictions on the domain. In this case, x - 5 = 0, so x = 5. Therefore, the domain of the function is all real numbers except x = 5.

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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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