Answer to Question #238991 in Discrete Mathematics for Joseph

Question

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).

Answer 1

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 n^x

Part iii

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