Hello having difficult on how to figure out domain rules. I have several homework problems I can remember how to solve. please help

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hello having difficult on how to figure out domain rules. I have several homework problems I can remember how to solve. please help

Expert Solution
Step 1

Functions are mathematical construcs that take inputs and give outputs. Sometimes, a function can give us indefinite outputs such as : infinity corresponding to a certain value of input. In other cases, the function does not give a meaningful value of does not exist for certain cases of inputs. Hence these values are not supposed to be entered into the function. The set of input values for which a function gives a finite output is called the domain of a function. Now let us see how to find domains for certain functions.

Step 2

Take for example fractional functions. 

In 1/x, if x =0, we get infinte. So the domain of x is all real numbers except zero

In the next exaple x cannot be equalt to 2 for the same reasons

In the final example, if x = 0 the exponent becomes 1, which then gives infinite. 

To find the domain in such functions you need to find the zeros of the denominator. Then the domain is all real values except the zeros

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