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Find the domain of the function.

$ f(x) = \dfrac{x + 4}{x^2 - 9} $

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$D :(-\infty,-3) \cup(-3,3) \cup(3, \infty)$

00:54

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

Idaho State University

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.

01:02

Find the domain of the fun…

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04:23

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01:04

Find the domain of the giv…

01:30

Find the domain of $f$.

01:15

we want 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, you want to focus on the denominator. Remember that division by zero is undefined, and so the denominator cannot be equal to zero. So let's figure out what numbers would make the denominator equal. Zero. If X squared minus nine was equal to zero, then X squared would be equal to nine and X would be equal to plus or minus three. So we're saying that those numbers cannot be in the domain and everything else can. So we have different ways of expressing the domain. One way is to use interval notation so we would have all the numbers from negative infinity to negative three round brackets showing that you're not including it union, Which means or and then all the numbers from negative 3 to 3 again round Brackett, showing that you're not including it and then union, which means or again, and then the interval from three to infinity. So that's one way of saying all real numbers except X equals three and X equals negative three

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