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Question 110923: f(x)=
x^2-3x-10
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x^-6x+9
--- means divided by
find the domain
and
find the x-intercepts
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!  Start with the given function
 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.
 Factor the left side (note: if you need help with factoring, check out this solver)
Now set each factor equal to zero:
 or
 or Now solve for x in each case
Since these two answers are the same, our only solution is
Since makes the denominator equal to zero, this means we must exclude from our domain
So our domain is: 
which in plain English reads: x is the set of all real numbers except 
So our domain looks like this in interval notation
\cup\left(3,\infty \right))
note: remember, the parenthesis excludes 3 from the domain
To find the x-intercepts, set the entire expression equal to zero
So this means the numerator can only equal zero
 Factor the left side (note: if you need help with factoring, check out this solver)
Now set each factor equal to zero:
 or 
 or  Now solve for x in each case
So our solutions are or
This means the x intercepts are (-2,0) or (5,0)
Notice if we graph , we can see that the x intercepts are (-2,0) or (5,0) and is not in the domain
So this verifies our answer.
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