If a function is defined as f(x,n) mod n. Determine the i. Domain of f ii. Range of f iii. G(g(g(g(7)))) if g (n) = f(209, n).

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Part i

The mod function we can only apply on integers

So, Domain $\{f(x,n)\}= Set \space of \space integers = \{...-2,-1,0,1,2...\}$

Part ii

Range of f(x,n)= {0,1,2,...n-1}

Because x and n = remainder when xn divided by nx

Part iii

$g(7)=f(209,7)= 209 mod 7= 6\\ g(g(7))=g(6)=f(209,6)= 5\\ g(g(g(7)))=f(209,5)= 4\\ g(g(g(g(7))))=f(209,4)= 5\\$