Question 62557
Find the Domain of the function:

{{{(x^4-2x^2+7)/(3x^2-10x-8)}}}
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^2-10x-8=0}}}
{{{3x^2-12x+2x-8=0}}}
{{{(3x^2-12x)+(2x-8)=0}}}
{{{3x(x-4)+2(x-4)=0}}}
{{{(3x+2)(x-4)=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!!!