+422 What is the domain of the function
j(x) = 1/(x+8) + 1/(x^2+8) + 1/(x^3+8)
Express your answer as a union of intervals.
+422 Oh wait nvm.
SOLUTION:
We note that j(x) is defined unless one or more of the denominators x+8, x^2+8, x^3+8 is equal to 0.
We have x+8=0 if x= -8, x^3+8 and if x= (cube root of -8)= -2. There is no real x for which x^2+8=0. Therefore, the domain of j(x)consists of all real x except and -8 and -2. As a union of intervals, this is...
(-∞ ,-8)∪(-8,-2)∪(-2,∞)
