In Exercises 1–8, find the domain of each rational function. h(x)...

Question

In Exercises 1–8, find the domain of each rational function. h(x)=(x+7)/(x^2−49)

Accepted Answer

considered to give a rational function. And finance domain experts. 12 over X squared minus 1 44. So you have x plus 12 over X squared minus 1 44. Now we have a rational function which means we have a polynomial on top of the polynomial on bottom to determine what our domain will be. We can go ahead and set our denominator equal to zero because we want to see if we have any discontinuities. We can find this continuity by setting our domain. I'm sorry denominator equal to zero and finding the domain. So let's go ahead and do that. We wanna take our X squared minus 1 44 square minus 44 and set it equal to zero. Now let's figure out what our X will be solved for X And 1:40 for both sides. X squared equals 1 44. Take the square the both sides. We will get X equals plus or minus 12 plus or minus because we have a positive and a negative answer with a square root. We can test this out by plugging it back into our original equation. Let's say. We checked 12 12 plus 12. 12 squared minus 1 44. That is 24 on the top. 12 squared is 1 44 that uses zero on the bottom. So this is a dis continuity with a division by zero. Now let's check our negative 12 negative 12 plus over negative 12 squared minus 1 44. That is 0/0. That is also this continuity. So we know our X values cannot equal positive 12 or negative 12. And those are the only restrictions we have on demand. So demand will be from the infinity To our first restriction negative 12 and Data 12 to our next restriction 12 And finally 12 to positive infinity. This is the equation aren't I mean? Or rather the list of values for them, in which means the answer to our problem is the answer. D. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 1–8, find the domain of each rational function. h(x)=(x+7)/(x^2−49)