SOLUTION: Find the domain of the function. (Enter your answer using interval notation.) f(x) = 5x3 − 5 x2 + 3x − 18

Algebra ->  Functions -> SOLUTION: Find the domain of the function. (Enter your answer using interval notation.) f(x) = 5x3 − 5 x2 + 3x − 18       Log On


   

Question 992573: Find the domain of the function. (Enter your answer using interval notation.)
f(x) =
5x3 − 5
x2 + 3x − 18
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to assume the function is f%28x%29+=+%285x%5E3-5%29%2F%28x%5E2%2B3x-18%29


Set the denominator equal to 0 and solve for x.


x%5E2%2B3x-18=0


%28x%2B6%29%28x-3%29=0


x%2B6=0 or x-3=0


x=-6 or x=3


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If x=-6 or x=3, then x%5E2%2B3x-18=0


To avoid division by zero, we exclude those values out of the domain. Any other x value is allowed.


Draw out a number line. Plot -6 and 3 on it. Those values will have open holes at them because we're excluding them from the domain.


So that means the answer in interval notation is