can someone help me find the doman of: f(x) = (3x-2) / (x^2 - x - 12)?

Answer 1

The domain is all real numbers where the denominator does not equal zero. So set the denominator equal to zero to find the excluded numbers of the domain.

f(x) = (3x - 2) / (x² - x - 12) = (3x - 2) / [(x + 3)(x - 4)]

x² - x - 12 = (x + 3)(x - 4) = 0

So the domain is:

(-∞, -3) U (-3, 4) U (4, ∞)

Answer 2

Domain is the limits on x, in a fraction the denominator can not be zero so factor the bottom to see when it is zero.
(x-4)(x+3)
so x can not be 4 or -3