domain of (4x^3 − 2) /(x^2 + 3x −18)

Question

what is the domain of (4x^3 − 2) /(x^2 + 3x −18) in interval notation?

Answer 1

Factor the denominator to find where it may be zero.

 

(4x³ - 2)/(x² + 3x - 18) = (4x³ - 2) / [(x + 6)(x - 3)]

 

You can see the denominator is zero at x = -6 and 3, so these are excluded from the domain, so the domain is all real numbers except -6 and 3.