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

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

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.

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

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)

Let f:N to N be defined by f(n)={{:((n+1)/2, " if n is odd"),(n/2, "if n is even"):} for all n in N . Prove that f is many-one, onto function.

Find the sequence of the numbers defined by a_n={1/n , when n is odd -1/n , when n is even

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

Let f: W ->W be defined as f(n) = n - 1 , if n 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.

check that f : N- N defined by f(n)={(n+1)/2,(if n is odd)),(n/2,(if n is even)) is one -one onto function ?

If composite function f_1(f_2(f_3((f_n(x))))n timesis an decreasing function and if 'r' functions out of total 'n' functions are decreasing function while rest are increasing, then the maximum value of r(n-r) is (a) (n^2-4)/4 , when n is of the form 4k (b) (n^2)/4, when n is an even number (c) (n^2-1)/4, when n is an odd number (d) (n^2)/4, when n is of the form 4k+2