In Exercises 1–30, find the domain of each function. g(x) = 2/(x+...

Question

In Exercises 1–30, find the domain of each function. g(x) = 2/(x+5)

Accepted Answer

Hello. Today we're gonna be finding the domain of a given function. So the function given to us is F. Of X. Is equal to negative 11 over X plus 29. So let's quickly recall how you find the domain of a rational function. If we have a rational function F of X is equal to one over X. The only value we cannot include for this function is zero because zero is going to cause a rational function to become undefined. What this means is every time you want to find the domain of a rational function you take your denominator and set it not equal to zero. And once you sell for X, you're going to find the value of X that causes your function to become undefined. So let's go ahead and do that. Our denominator is the quantity X plus 29. And we don't want that to equal to zero. Now we need to go ahead and solve this equation for X. So that we can find the value that causes our function to become undefined. In order to solve for X. I'm gonna go ahead and subtract 29 from both sides of this equation. Doing so is going to give me X is not equal to negative 29. Now, what this statement means is that we can include any value of X into this function but the only value we cannot include is -29. So representing that on a line graph, we have the value of negative 29. We can include all the values that come before negative 29 after negative 29 but we cannot include the value negative itself. So how do we represent that in interval notation? Well, what this means is we want all the values from negative infinity up until negative 29. So we're gonna go from negative infinity to negative 29 without including it. So we're gonna use a parentheses And we want all the values not including -29 and everything that comes after to infinity. So we're going to use a parentheses And we want all the values not including -29 to positive infinity. So we have two regions of solutions. But how do we unite those regions together While we just go ahead and use the union symbol And this is going to be the domain of this rational function, negative infinity to negative 29 Union -29 to infinity. So this is the domain in interval notation. And that means that the answer to this problem is going to be a So I hope this video helps you in understanding how to find the domain of a rational function. And I'll go ahead and see you all in the next video

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