If `f:{1,2,3....}->{0,+-1,+-2...}` is defined by `f(n)={n/2, if n ` is even , ` -((n-1)/2) if n ` is odd `}` then `f^(-1)(-100)` is

If f:{1,2,3...}rarr{0,+-1,+-2...} is defined by f(n)={(n)/(2), if n is even -((n-1)/(2)) if n odd } then f^(-1)(-100) is

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) .

Let f:N uu{0}rarr N uu{0} be defined by f(n)={n+1, if n is eve nn-1,quad if quad n is odd Show that f is a bijection.

If f:N rarr N is defined by f(n)=n-(-1)^(n), then

Let f : N to N : f (n) = {underset((n)/(2), " when n is even ")( (1)/(2) (n+1) , " when n is odd ") Then f is

If f(n)=1^2+2.2^2+3^2+2.4^2+5 .6^2+2.6^2+...+ n terms ,then (A) f(n)= (n(n+1)^2)/2 , if n is even (B) f(n)= (n^2(n+2)^2)/2, if n is even (C) f(n)= (n^2(n+1))/2 , if n is odd (D) f(n)= (n(n+3)^2)/2 if n is odd

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.

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

f_(n)={{:(f_(n-1)" if n is even"),(2f_(n-1)" if n is odd"):} and f_(o)=1 , find the value of f_(4)+f_(5)