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

f(x,n)=x mod n

domain f=Z$\times N$

range f=$Z^+=N\cup\lBrace 0 \rBrace$

g(7)=209 mod 7=[209=29$\cdot$ 7+6]=6;

g(g(7))=209 mod 6=[209=34$\cdot$ 6+5]=5;

g(g(g(7)))=g(5)=209 mod 5=[209=41$\cdot$ 5+4]=4;

g(g(g(g(7))))=g(4)=209 mod 4=[52$\cdot 4+1]=1$

So g(g(g(g(7))))=1.