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Question 553906: What is the domain of (3x+60)/(x^2-144)?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! In this function, there is a DENOMINATOR, and denominators must NEVER equal zero!
The first step, whenever you see a denominator, is to set that denominator equal to zero in order to see what the FORBIDDEN values are!
In this case, x^2-144 = 0, which is a quadratic equation. There are TWO solutions:
x^2 = 144
x=12 or x=-12
Now, these are the FORBIDDEN values. Domain means what values of x ARE allowed? The answer is all values of x EXCEPT 12 and -12.
For a NON-TRADITIONAL explanation of Functions, Domain and Range that is probably easier to understand than your own textbook, please see my own website! The easiest way to find it is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the very bottom of this page there is a link that will take you to the Homepage of my website. I have a complete ALGEBRA curriculum there with LOTS of practice tests, and even a few videos. Best of all, it's all FREE!!!
For this particular topic, when you find the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", choose "Intermediate Algebra" and look in Chapter 5, or you can choose "College Algebra" and look in "Chapter 2" for the sections called "Functional Notation, Functions, Domain, and Range." There is a complete explanation, together with lots of examples and exercises with ALL the answers given. You will especially like the "Math in Living Color" pages that go with this, where most of the hardest exercises are solved for you IN COLOR! I even have videos of me teaching this topic in both Intermediate and College Algebra before I retired. To see the videos, look on my Homepage for "Rapalje Videos in Living Color." Remember, it's all FREE!
If you or anyone needs to contact me, my Email address is rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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