Mathematics

Mathematics

Problem

Let h(x)=(x2−4)(x−5)(x+2)(x2−9).h(x)=\dfrac{(x^2-4)(x-5)}{(x+2)(x^2-9)}. Determine the domain of hh. a) R∖{−3,3}\mathbb R\setminus\{-3,3\} b) R∖{−2,3}\mathbb R\setminus\{-2,3\} c) R∖{−2,−3,3}\mathbb R\setminus\{-2,-3,3\} d) R∖{−2,−3,3,2}\mathbb R\setminus\{-2,-3,3,2\}
Intuitive explanation

The domain of a rational function is all real numbers except where the denominator equals zero. Factor the denominator completely, then solve for which xx-values make it zero—those are the values you must exclude. Pay attention to whether any factors cancel with the numerator, since a removable discontinuity (hole) is still excluded from the domain.

Intuitive explanation

The domain of a rational function is all real numbers except where the denominator equals zero. Factor the denominator completely, then solve for which xx-values make it zero—those are the values you must exclude. Pay attention to whether any factors cancel with the numerator, since a removable discontinuity (hole) is still excluded from the domain.

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