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Problem 36 Hard Difficulty

Find the domain of the function.

$ f(u) = \dfrac{u + 1}{1 + \frac{1}{u + 1}} $

Answer

$(-\infty,-2) \cup(-2,-1) \cup(-1, \infty)$

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Video Transcript

we're going to find the domain of this function and remember that the domain is the set of rial number inputs that would yield rial number outputs. And when you're looking at a rational function like this, what you want to focus on is that the denominator cannot be zero. Because if you divide by zero, that's undefined. So we have a couple of denominators to look at here. First of all, we have the denominator of our little fraction. So we know that that denominator cannot be zero. So you plus one cannot be zero. And that means that you cannot be negative one. Okay, so that takes care of one exclusion from the domain. But we also have this larger denominator here, and so one plus one over U plus one cannot equal zero. That means that one over U plus one cannot equal negative one. And that means that you cannot equal negative too. So we know what you cannot be now for the domain. Let's say what you can be. So we're going through all real numbers except for negative one and negative too. So we have the interval from negative infinity, too. Negative, too. Union the interval from negative to to negative one union the interval from negative one to infinity. Remember to use the round brackets to show that you're not including the endpoints.