Science:Math Exam Resources/Courses/MATH100/December 2015/Question 01 (iv)
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Question 01 (iv) 

Describe all points where the function is continuous. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

What are the domain of continuity for the functions , , and ? 
Hint 2 

Recall that if and are continuous at , then is also continuous at . Furthermore, if , then is continuous at . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Note that , , and are continuous on . By the statement in Hint 2, this implies that is continuous on . Also, the function is continuous at , because for any . Actually, when , the given function is undefined because the denominator is zero. Therefore, the answer is . 