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Question 913278: what is the domain for y=4/x^2+1?
Answer by tutoringisfun(17)   (Show Source):
You can put this solution on YOUR website! 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.
I hope this was helpful to you. If you desire PAID assistance, you can contact me at http://www.prestoexperts.com/expert/marys-tutoring or via my facebook page listed in my profile or you may leave me a message via www.instaedu.com Have a great day!
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