SOLUTION: Find the Domain of the function: (x^4 - 2x^2 +7)/ (3x^2 -10x -8)

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Question 62557This question is from textbook
: Find the Domain of the function:
(x^4 - 2x^2 +7)/ (3x^2 -10x -8) This question is from textbook

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find the Domain of the function:
%28x%5E4-2x%5E2%2B7%29%2F%283x%5E2-10x-8%29
The domain is what x is allowed to be. There is a restriction for x in rational functions. x can be anything EXCEPT what will make the denominator =0.
3x%5E2-10x-8=0
3x%5E2-12x%2B2x-8=0
%283x%5E2-12x%29%2B%282x-8%29=0
3x%28x-4%29%2B2%28x-4%29=0
%283x%2B2%29%28x-4%29=0
3x+2=0 and x-4=0
3x+2-2=0-2 and x+4-4=0+4
3x=-2 and x=4
3x/3=-2/3 and x=4
x=-2/3 and x=4
x cannot equal -2/3 or 4
The domain in set builder notation is:
{x|x not=-2/3,4} <---set builder notation
(-infinity,-2/3)U(-2/3,4)U(4,infinity)
Happy Calculating!!!