Maths problem set 1  Mathematics homework help

Prove that is onetoone function.

Let f:, as given below. Is f a onetoone function? Please explain why or why not.

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.
 If n is fixed as 5, is this function onetoone?
 List five numbers that have the exact same image.

Find

Find

Find

Find as

Prove that is a continuous function.

Find derivatives of the following functions using differentiation rules. (Do not use the definition of a derivative!)

Find the derivative of the following function at :

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)

Let and , where. Find and as well as the domain and range of these functions.

Find the derivative of by using the definition of the derivative
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