Question 913278
Good Morning student. 

Before I help you solve this problem, I feel that I have to review what we know about domains. When Y is a function of x, the domain is all the possible values for x. We cannot divide by 0 and we cannot take the root of a negative number. With those 2 rules in mind we can solve our problem. 

y=4/x^2 + 1

since the denominator has an x in it we can set the denominator equal to zero and solve for x as follows:

x^2 + 1=0 we want to isolate x so we have to subtract 1 from each side:
     -1 -1 this makes the 1's on the left cancel out and we are left with the following:

x^2= -1

to isolate x we have to take the square root of -1.

x=no real solution
According to the rules above we cannot take the root of a negative number. There is no real number for this equation, only imaginary numbers. Therefore, x is any real number. 

This means that the domain is all real numbers. It can be written in interval notation like this:
(-inf,inf) inf means infinity. 

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