g(3n+1)=3n+2 g(3n+2)=3n+3 g(3n+3)=3n+1, for all n≥0 g:N→N g(1)=2,g(4)=5,g(7)=8 g(2)=3,g(5)=6,g(8)=9 g(3)=1,g(6)=4,g(9)=7 ⇒f[g(1)]=f(1) ⇒f(2)=f(1) Clearly, it is not a one - onefunction. Now, f[g(2)]=f(2) f(3)=f(2) And, f[g(3)]=f(3) f(1)=f(3) Similarly, f[g(4)]=f(4) f(5)=f(4) And, so on lf(1)=f(2)=f(3) f(4)=f(5)=f(6)
Now, there can be a possibility such that So,f(x) can be onto function. When f(1)=f(2)=f(3)=1 f(4)=f(5)=f(6)=2 and so on.