f(x) = (x-8)/(x2+5x-24)
Factor the quadratic in the denominator:
f(x) = (x-8)/(x+8)(x-3)
In math(s), division by zero is undefined. So any value of x that makes the denominator of f(x) equal to zero will make f(x) undefined. Those values of x will be excluded from the domain of f(x). The denominator of f(x) = 0 when x = -8 and x = 3. The domain of f(x) then is all real numbers except x = -8 and x = 3. In interval notation:
(-∞, -8)U(-8,3)U(3,∞)
