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Problem 32 Hard Difficulty

Find the domain of the function.
$$ f(x) = \dfrac{2x^3 - 5}{x^2 + x - 6} $$


$(-\infty,-3) U(-3,2) U(2, \infty)$

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Video Transcript

we're going to find the domain of this function and remember that the domain would be the set of rial number inputs that yield rial number outputs. And when you're looking at a rational function like this, you want to focus on the denominator because we know that we can't divide by zero division by zero is undefined. We need to focus on what numbers make the denominator zero and exclude those from the domain. So what numbers would make X squared plus X minus six equal zero? What? What if we factor that into X plus three times X minus two and set each factor equal to zero and salt Each of these equations We would have X equals negative three and X equals two. So these are the numbers that cannot be in the domain because they would make the denominator zero. So then, what is in the domain? All the other real numbers. So that would be all real numbers that go from negative infinity to negative three Union negative 3 to 2 union to to Infinity Union means or and the round brackets mean you're not including the endpoint