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Question 498777: Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations.
F(x)=16x/(x^2+9)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The domain of a function is the set of values of the independent variable ( , in this case) for which the function is defined. Rational functions are undefined for any value of the variable that would cause the denominator to equal zero.
So set the expression in the denominator equal to zero and solve. The value or values in the solution set, if any, will be the value or values that are excluded from the domain. In your case, the denominator function is a quadratic polynomial that has two real number roots. Until you solve  , let us refer to these roots as  and  and presume without loss of generality (the subscripts are arbitrary) that 
Your domain, in interval notation, is a rather clumsy: \ \small\cup\Large\ \left(\varphi_1,\varphi_2\right)\ \small\cup\Large\ \left(\varphi_2,\infty\right))
In fact, set builder notation is much more descriptive, IMHO:
John
My calculator said it, I believe it, that settles it
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