SOLUTION: Find the domain of f(x)= (2x + 3)/(2x^2 - 3x - 27). Leave your answer in interval notation.

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Question 62271: Find the domain of f(x)= (2x + 3)/(2x^2 - 3x - 27). Leave your answer in interval notation.
Answer by funmath(2933) About Me  (Show Source):
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Find the domain of f(x)= (2x + 3)/(2x^2 - 3x - 27). Leave your answer in interval notation.
This is a rational function, the x values in rational functions have the restriction of not being anything that causes the denominator (bottom of a fraction) to =0.
2x%5E2-3x-27=0
2x%5E2%2B6x-9x-27=0
%282x%5E2%2B6x%29%2B%28-9x-27%29=0
2x%28x%2B3%29-9%28x%2B3%29=0
%28x%2B3%29%282x-9%29=0
x+3=0 and 2x-9=0
x=-3 and 2x=9
x=-3 and x=9/2
This function is undefined at x=-3 and x=9/2. Therefore the domain is:
(-infinity,-3)U(-3,9/2)U(9/2,infinity) <---interval notation.
This just means that x can be any real number as long as it's not -3 or 9/2.
Happy Calculating!!!