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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.

 Jan 30, 2019
 #1
avatar+409 
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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,∞)

 Jan 30, 2019

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