Question 133984
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?