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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?
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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?
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