State in interval notation the domain of f(x) = [x+4/(x^2+2x-8)]

Answer 1

Hi Melissa,

The domain of a function is the set of all possible x values where the function is defined.

If we factor the polynomial in the denominator, we can re-write our function as:

f(x) = (x + 4) / (x + 4)(x - 2)

EDIT: Thanks to the commenters below. Since we cannot divide by 0, our function is defined for all value of x, except when x = 2 and x = -4. We are unable to cancel out the (x+4) term in the numerator and denominator as it would falsely omit the "hole" at x = -4.

Using interval notation, we can say that our domain is ( -∞, -4) ∪ ( -4, 2 ) ∪ ( 2, ∞ ).