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4.2 Domain of the rational function

The domain of a rational function is defined as those values of x for which the function is always defined and does not take the form of any indefinite form.

Now the roots of the denominator are obviously x = 4 and x = -3. That is, if x takes on either of these two values, the denominator becomes equal to zero. So the function is not defined for these two values of x. We say that the function is discontinuous at x = 4 and x = -3 and is continuous at all other values for x. In other words, all real numbers except 4 and -3 are allowed as inputs to this function.

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The domain for the function, therefore, as expressed in interval notation is:

(-∞, -3) U (-3, 4) U (4, + ∞)

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