`f: Z -> Z and g : Z -> Z` are defined as follows: `f(n) =(n+2` , n even and `2n-1`, n odd and `g(n) = (2n` ,n even and `(n-1)/2` , n odd, Find `fog` and `gof`.

f: Z rarrZ and g : Z rarrZ are defined as follow : f(n) ={:{(n+2," n even"),(2n-1," n odd"):}, g(n) ={{:(2n,"n even"),((n-1)/2,"n odd"):} Find fog and gof.

The function f:NrarrZ defined by f(n)=(n-1)/(2) when n is odd and f(n)=(-n)/(2) when n is even, is

Let f: N->N be defined0 by: f(n)={(n+1)/2, if n is odd (n-1)/2, if n is even Show that f is a bijection.

On the set Z of all integers define f : Z-(0) rarr Z as follows f(n)= {(n/2, n \ is \ even) , (2/0 , n \ is \ odd):} then f is

Let f: N rarr N be defined by : f(n) = {:{((n+1)/2, if n is odd),(n/2, if n is even):} then f is

Consider f : N ->N , g : N ->N and h : N ->R defined as f (x) = 2x , g (y) = 3y + 4 and h (z) = sin z , AA x, y and z in N. Show that ho(gof ) = (hog) of.

Consider f : N ->N , g : N ->N and h : N ->R defined as f (x) = 2x , g (y) = 3y + 4 and h (z) = s in z , AA x, y and z in N. Show that ho(gof ) = (hog) of.

If n (ne 3) is an integer and z = -1 + isqrt3 , then z^(2n) + 2^(n) , z^(n) + 2^(2n) =

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }