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

Suppose the function gives the accumulated rainfall in millimetres minutes into a sudden rainstorm. Is invertible? Explain why or why not. 
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 

Recall that in order to have an invertible function, we must have a onetoone function, i.e. remains a function in the reverse direction, that is each can be corresponded to only one single . 
Hint 2 

Note that since is the accumulated rainfall, it is an increasing function. Is it possible to have the same amount of rainfall in two different times? 
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. We need to check if the function is onetoone, i.e. if all values can be corresponded to only one value. Since is the accumulated amount of rainfall in a thunderstorm so it is an increasing function, this means that it is not possible to have equal amount of rainfall in two different times, therefore, this function is onetoone and hence invertible. 