Science:Math Exam Resources/Courses/MATH110/December 2015/Question 01 (b)
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Question 01 (b) 

Consider a function such that for and for . Let . Determine the sign of the composite function if and if . 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

What is the sign of ? How would the sign of help us determine the sign of ? 
Checking a solution serves two purposes: helping you if, after having used the hint, 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. Take , since this is a square function it is always nonnegative, i.e. whether or , . Thus the composite function is negative i.e. because . Answer: In both case, . 