Show that `f: N->N` defined by `f(n)={(n+1)/2,\ \ if\ n\ i s\ od d n/2,\ if\ n\ i s\ e v e n` is many-one onto function.

Show that f:n rarr N defined by f(n)={(((n+1)/(2),( if nisodd)),((n)/(2),( if niseven )) is many -one onto function

Let f: NvecN be defined by f(n)={(n+1)/2, "if" n "i s o d d"n/2, "if "n "i s e v e n" for a l l n N} Find whether the function f is bijective.

Show that f : NvecN , given by f(x)={x+, if x i s od dx-1, if x i s e v e n is both one-one and onto.

Let f:N->N be defined as f(n)= (n+1)/2 if n is odd and f(n)=n/2 if n is even for all ninN State whether the function f is bijective. Justify your answer

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

Show that the function f:N rarr Z, defined by f(n)=(1)/(2)(n-1) when n is odd ;-1/2 n when n is even is both one-one and onto

Let f: Z->Z be given by f(x)={x/2,\ if\ x\ i s\ e v e n,0,\ if\ x\ i s\ od d . Then, f is (a) onto but not one-one (b) one-one but not onto (c) one-one and onto (d) neither one-one nor onto

Let f:N rarr N be defined by: f(n)={n+1,quad if n is oddn -1,quad if n is even Show that f is a bijection.

Let f" ": N->N be defined by f(n)={(n+1)/2,""if""""n""""i s""""odd" " n/2,""if""""n""""i s""e v e n for all n in N . State whether the function f is bijective. Justify your answer.