Final answer:
The function f(x) = (x+3)/(x²+5x-24) is discontinuous at x = 3 and x = -8.
Step-by-step explanation:
The function f(x) = (x+3)/(x²+5x-24) is discontinuous at any value of x where the denominator is equal to zero. Therefore, to find where the function is discontinuous, we need to find the values of x that make the denominator zero.
First, let's factor the denominator. The quadratic equation x²+5x-24=0 can be factored as (x-3)(x+8)=0. This means that the denominator is equal to zero when x=3 or x=-8.
Therefore, the function f(x) is discontinuous at x=3 and x=-8.