restrictions on domain precalcluls quesiton

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

Explain the restrictions on the domain of F(x)=log(x-5)+1 - if there are any. 

Explain the restrictions on the domain of    (the cube root of x-2) +3  -if there are any. 

Sep 2nd, 2015

Thank you for the opportunity to help you with your question!

1. To take the 'log' of a number, it must be greater than zero.  You can look at the graph to see that the 'log' graph is never a negative x-value, or you can try taking the 'log' of a negative number in your calculator, and it should come back undefined.  So you can set the inner part of the log greater than zero.

x-5>0

x>5

So, domain is: (5,infinity)


2. For all cubed roots, there are no restrictions to the domain.  It's a simple rule you can just memorize.  The reason this works is because you can multiply three negative numbers with each other to get a negative number, so the inner part of the cubed root can be negative.  The inner part of a square root cannot be negative though.

Domain: (-infinity, +infinity)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 2nd, 2015

in addition, for F(x)=(e^x+4) +7, is there a value that would cause the function to be undefined? Are there restrictions of the domain/explain- if not explain why. 



Also, for both of the first 2, are there any values of x that would cause the function to be undefined? 

Sep 2nd, 2015

Domain for e^x is all real numbers, so (x+4) can equal anything.  No restrictions on the domain.  You can also see from the graph that the domain of x is (-infinity,+infinity).  The range, however, is limited.

For the first two, there are no other values of x that would cause the function to be undefined.

Do you need ranges as well, or just domains?

Sep 2nd, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Sep 2nd, 2015
...
Sep 2nd, 2015
Jun 23rd, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer