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Question 553484: Find the domain of the function g(x)=3/10-7x
Found 2 solutions by rapaljer, nyc_function:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Domain means the set of all possible x values. It is basically the set of all real numbers but EXCLUDING all values that are not allowed, mostly due to DENOMINATORS and SQUARE ROOTS! In this case, the denominator is 10-7x, which must NOT equal zero. Therefore, the DOMAIN is the set of all real numbers, EXCEPT the value that makes the denominator = 0.
10-3x=0
10=3x
10/3=x
Domain is all real values EXCEPT 10/3.
I wrote a whole NON-TRADITIONAL explanation of DOMAIN and RANGE in both Intermediate and College Algebra!! The easiest way to find my explanation is to go to my FREE website using the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the bottom of this page is a link that will take you to my Homepage. Look near the top of this page for the link "Basic, Intermediate, and College Algebra: One Step at a Time", click on either "Intermediate Algebra" or "College Algebra." In Intermediate Algebra look in Chapter 5 for the section "5.06 Functions Domain and Range." In College Algebra, look in Chapter 2 for section "2.07 Functions Domain and Range". The lesson is complete with explanations, examples, and exercises with all the answers. You will especially like the "MATH IN LIVING COLOR". There is also a FREE video of me teaching this topic in my younger years before I retired from teaching. The video can be found from my Homepage by looking for the link "Rapalje Videos in Living Color". Choose either Intermediate or College Algebra, and look for the video called "FDR (Functions, Domain, and Range)." I think you will find that my explanations are a LOT easier to understand than the traditional textbooks you are probably using.
Happy New Year!! My Email address is rapaljer@seminolestate.edu if you need to contact me!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by nyc_function(2741)  (Show Source):
You can put this solution on YOUR website! To find domain for g(x), set denominator to zero and solve for x.
10 - 7x = 0
-7x = -10
x = -10/-7
x = 10/7
DOMAIN = ALL REAL NUMBERS EXCEPT THAT X CANNOT EQUAL 10/7.
WHY CAN'T X = 10/7 HERE?
If x is replaced by the fraction 10/7, division by zero is made.
Since division by zero does not exist, x CANNOT BE 10/7.
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