To find the domain, we know that the denominator can never equal 0, so 15 - ^2 X ^2 - 64 can never equal 0. We also know that inside of a square root has to be positive or zero. So we need to solve each of these individually and then look to see where these two intersect as far as their domains go. So we know 15 can't equal sqrt X ^2 -, 64 square each side, so 225 can't equal X ^2 - 64. So X ^2 is not going to equal 289. So X isn't going to equal the positive and negative sqrt 289. So sqrt 289 is 17. So from there we're going to we're going to solve the other one. So X isn't going to equal positive or -17. Here we know that X ^2 - 64 is greater than or equal to 0. So if I take that 64 to the others. Now let's do difference of squares X -, 8 X plus X -, 8 * X + 8 greater than or equal to 0. If we thought about looking at our number line here, we'd have a. We'd have a +8 and a -8 as my intercepts. This is a parabola. It's going up because the leading coefficients positive. So if I want the places that it's greater than or equal to 0, I need the YS that are positive. So I'd say -8 negative Infinity to -8 union, union 8 to Infinity. So now when I look at these, I need to have where they're both true. So we'd have negative Infinity to -17 union -17 to -8, and it's going to be a bracket because that -8 didn't force there to be a zero in the denominator. Union 8 to 17. Union 17 to Infinity.