Pre Calculus

Question

For the rational function f(x)=(x²-1)/(x³+9x²+14x), find the domain.

a) (-∞, -7)∪(-7, -2)∪(-2, ∞)

b) (-∞, -7)∪(-7, -2)∪(-2, 0)∪(0, ∞)

c) (-∞, 0)∪(0, ∞)

d) (-∞, 0)∪(0, 2)∪(2, 7)∪(7, ∞)

 

Answer 1

Factor the denominator x(x+7)(x+2).  The domain is all real numbers except for those for which the denominator is zero which would exclude 0,-7, and -2. 

Expressed in interval notation, the answer is b) above.