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Find the domain of the function.

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

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

01:29

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Johns Hopkins University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

02:06

Find the domain of the fun…

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01:31

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01:21

Find the domain of $f$.

00:23

Determine the domain of th…

01:03

Find the domain of the giv…

01:10

00:28

00:39

00:17

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.

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