Given the function f(x)=4x/sqrt of (x-4), find the domain.

Question

So I have

f(x)=       4x__

           √x-4

 

 

I sort of know how to go about this. I solved for x, and I got that x>4 as my answer, but in my answer I have to write it as a linear point with the domain and range (x,y). If 4 is my x, what would the y be and how do I determine that? Any information for future reference would be greatly appreciated. Thank you!

Answer 1

Olesya, I think you are slightly confused on the (x,y). Your domain is your input, so we are not worried about y. What you may be thinking of is interval notation, which includes parentheses but does not mean a certain point.

 

Let's say we had an answer like 3 <x < 8. This would be written as (3,8) in interval notation.

 

If something is included, though, then we use a bracket. 3 < x < 8 would be written as [3,8)

 

In your case, since we have x > 4, then we can go as high as we want- all the all to infinity. Since infinity is not a number, it's never included. Our answer is (4,∞).

 

Again, what is inside the parentheses is the bounds of our x. We can do the same thing with the range, find the bounds of our y, and write it the exact same way. I hope this makes sense.