SOLUTION: find the domain of f(x)=1/(x^2-2x-15)

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Question 1077353: find the domain of f(x)=1/(x^2-2x-15)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=1%2F%28x%5E2-2x-15%29+
f%28x%29=1%2F%28x%5E2%2B3x-5x-15%29+
f%28x%29=1%2F%28%28x%5E2%2B3x%29-%285x%2B15%29%29+
f%28x%29=1%2F%28x%28x%2B3%29-5%28x%2B3%29%29+
f%28x%29=1%2F%28%28x-5%29%28x%2B3%29%29+
recall that denominator cannot be equal to zero; so, we need to exclude the values of x that make denominator equal to zero
%28x-5%29%28x%2B3%29=0+
if %28x-5%29=0+=>x=5
or if %28x%2B3%29=0+=>x=-3
so, domain is all real numbers x except x=5 and x=-3

{ x element R : x%3C%3E-3 and x%3C%3E5 }