In Exercises 1–30, find the domain of each function. f(x) = 1/(x+...

Question

In Exercises 1–30, find the domain of each function. f(x) = 1/(x+7) + 3/(x-9)

Accepted Answer

Welcome back. I'm so glad you're here. We have this function F of X equals four divided by X plus eight minus six divided by x minus three. And we are asked to find the domain. Well how do we find the domain? We take a look at our function and we see if there are any possible domain restrictions going on here. And in this case we've got two fractions and those fractions can't have a zero in the denominator. Otherwise they would be undefined. So what we do to find out what would make those denominators zero is set each of those denominators equal to zero. So X plus eight equals zero and x minus three equals zero. We solve for X and then we'll know what values make our denominators zero and therefore having undefined fractions. So let's subtract eight from both sides. For X plus eight equals zero. That will give us X equals negative eight. For x minus three equals zero. Let's add three to both sides. And that will give us X equals three. And what does that mean? That means if X equals negative eight will have a zero in the denominator. And if X equals three will have a zero in the denominator. So that means our domain restriction is that X can be all real numbers except negative eight and three. So, to express that in interval notation we start with the parentheses going from negative infinity. All the way up to negative eight. But closing with the parentheses because we can't include negative eight in union with. And starting again at negative eight because it can be all the other numbers um from negative eight up to three, again closing with the parentheses in union with and again starting with the parentheses and three because it can be all those other numbers all the way up to positive infinity. Closing with the parentheses because we can never actually get to infinity, we look at our answer choices and this matches with answer choice. A well done, we'll catch you on the next one.

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