SOLUTION: Find the domain of the following function f(x)=x+5/x^2-4 Can you please explain how to work this out!!

Question 316118: Find the domain of the following function
f(x)=x+5/x^2-4
Can you please explain how to work this out!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The domain is the set of all values that we can plug in for 'x' which will give us some number output for f(x)

Since you CANNOT divide by zero, this means that we must look for values that make the denominator equal to zero. So just set it equal to zero and solve.

Set the denominator equal to zero.

Add 4 to both sides.

Take the square root of both sides. Don't forget about the plus/minus.

or Break up the plus/minus.

or Take the square root of 4 to get 2.

So when or , the denominator is equal to zero.

To avoid dividing by zero, we then make the restriction that or

So the domain of is the set of all real numbers but or

In interval notation, we would write that as:

Basically, we're taking the number line and picking out the numbers -2 and 2.
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