SOLUTION: find domain f(x)= x^4-2x^3+7 / 3x^2-10^x-8

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Question 97438: find domain
f(x)= x^4-2x^3+7 / 3x^2-10^x-8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+%28x%5E4-2x%5E3%2B7%29+%2F+%283x%5E2-10x-8%29 Start with the given function


3x%5E2-10x-8=0 Set the denominator equal to zero

%28x-4%29%283x%2B2%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:

x-4=0 or 3x%2B2=0

x=4 or x=-2%2F3 Now solve for x in each case


Since x=4 or x=-2%2F3 make the denominator equal to zero, that means we must exclude these values from the domain.

So our domain is: x is the set of all real numbers except x%3C%3E4 or x%3C%3E-2%2F3


Which looks like this in interval notation: