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# LET F:, AS GIVEN BELOW. IS F A ONE­TO­ONE FUNCTION? PLEASE EXPLAIN WHY OR WHY NOT.

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Author: Christine Farr
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1. Prove that is one­to­one function. 2. Let f:, as given below. Is f a one­to­one function? Please explain why or why not.3. The modulo function (a mod n or a modulo n) maps every positive integer number to the remainder of the division of a/n. For example, the expression 22 mod 5 would evaluate to 2 since 22 divided by 5 is 4 with a remainder of 2. The expression 10 mod 5 would resolve to 0 since 10 is divisible by 5 and there is not a remainder.a. If n is fixed as 5, is this function one­to­one? b. List five numbers that have the exact same image. 4. Find 5. Find 6. Find 7. Find as 8. Prove that is a continuous function. 9. Find derivatives of the following functions using differentiation rules. (Do not use the definition of a derivative!)a.b. c.d.e.f. g.h.10. Find the derivative of the following function at :  11. Find the derivative of the following function using the definition of a derivative. (Hint: though you can use the rules of differentiation to check your answer, you must use the definition of a derivative to solve this problem in order to receive any credit for your response)12. Let and , where. Find and as well as the domain and range of these functions.13. Find the derivative of by using the definition of the derivative

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