If `f:NrarrZ f(n)={(n-1)/2;` when n is odd `=-n/2;` when n is even Identify the type of function

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: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:N to Z and f (x)=[{:((x-1)/(2),"when x is odd"),(-(x)/(2),"when x is even"):}, then:

If f:NrarrZ defined as f(n)={{:((n-1)/(2),":"," if n is odd"),((-n)/(2),":", " if n is even"):} and g:NrarrN defined as g(n)=n-(-1)^(n) , then fog is (where, N is the set of natural numbers and Z is the set of integers)

lf a_(n)={ {:(n^(2), "when n is odd"),(2n,"when n is even "):} then write down ten beginning from the fifth term .

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

The value of i^(1+3+5+...+(2n+1)) is (1) if n is even,-i if n is odd (2)1 if n is even -1 if n is odd (3)1 if n is odd -1 if n is even (4) none of these

Let f:" "W ->W be defined as f(n)" "=" "n" "-" "1 , if is odd and f(n)" "=" "n" "+" "1 , if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.