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

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter1: Introduction To Algebra
Section1.1: Variables
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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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