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Question 553743: what's the domain of 3 root of (x-4)/ x-4
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! By "3 root of" I am assuming that you mean CUBE ROOT OF. Having said this, there are no restrictions on cube roots, so the only restriction in this problem is the DENOMINATOR! The denominator must NOT equal ZERO.
Set the denominator equal to zero to determine what value(s) are forbidden!
x-4=0, so x=4 is forbidden!
Therefore, the domain is ALL REAL VALUES of x, except the value of x=4.
For a NON-TRADITIONAL explanation of DOMAIN 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" for "Section 5.06 Functions, Domain, and Range Equations." Or, choose "College Algebra", and look in "Chapter 2" for "Section 2.07 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 many of the hardest exercises are solved for you IN COLOR! I even did a video on this topic before I retired. To see the video, look for "Rapalje Videos in Living Color" on my Homepage, and click on Intermediate Algebra" or "College Algebra". As I said, everything on this website is FREE! No pop-ups or advertising!!
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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