SOLUTION: Ok I've been working this problem for about 30 minutes and need your help. Find the domain of the function h(x)=x-3/x³-16x

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 Question 133984: Ok I've been working this problem for about 30 minutes and need your help. Find the domain of the function h(x)=x-3/x³-16x Answer by nycsharkman(136)   (Show Source): You can put this solution on YOUR website!Find the domain of the function h(x)=x-3/x³-16x The domain of a function is the collection of numbers that can be safely plugged into the function. We factor the denominator of your fraction. x(x^2 - 16) We now set to zero to find which numbers x CANNOT equal to in this function. x = 0 x^2 - 16 = (x - 4)(x + 4) x - 4 = 0 x = 4 x + 4 = 0 x = -4 I just found that when x = 0, -4 or 4, the original function becomes UNDEFINED. Why undefined? When you plug the numbers 0, -4 and 4 into the original function given, division by zero is created and this cannot take place in math. What is the domain? The domain is: ALL REAL NUMBERS EXCEPT 0, -4 and 4. Is this clear? =================================================== When I say the domain of your function is ALL REAL NUMBERS except 0, -4 and 4, I DO NOT mean (-infinity, infinity). The symbol (-infinity, infinity) actually means that the domain is ALL negative and positive numbers. Of course, this does not make sense for your question. Here is another way to say the above: The domain is: ALL REAL NUMBERS such that x CANNOT EQUAL 0, -4 and 4. Is this clear?