11. Suppose f NN satisfies the recurrence relationf(n)if f(n) is even3f(n)1 if f(n) is oddf(n1)2Note that with the initial condition f(0) 1, the values of the function are:f(1) 4 f(2)2. f(3) 1. f(4) 4 and so on, the images cycling throughthose three numbers. Thus f is NOT injective (and also certainly not surjective).Might it be under other initial conditions? 3If f satisfies the initial condition f(0) 5, is finjective? Explain why orgive a specific example of two elements from the domain with the sameimage.b. If f satisfies the initial condition f(0) 3, is f injective? Explain why orgive a specific example of two elements from the domain with the sameimage.c. If f satisfies the initial condition f(0) 27, then it turns out thatf(105) 10 and no two numbers less than 105 have the same image.Could f be injective? Explain.d. Prove that no matter what initial condition you choose, the functioncannot be surjective.

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This question is a multi part question. A, B, and C have all been answered.  I was instructed to ask again for D to be answered.

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Step 1

Given mapping and recurrence relation are,

Step 2

(a)If f satisfies the initial condition f (0) = 5, then

Step 3

Since, the value of the function is same at di...

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