`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.

Function f:NtoZ,f(n)={(n/2",","n even"),(-((n-1)/(2))", ","n-odd"):}

f : Z rarr Z and g : Z rarr Z . Defined as f(n) = 3n and g(n) = {{:(n/3",","If n is a multiple of 3"),(0",","If n is not a multiple of 3"):} AAninZ Then show that gof = I_z but fog ne I_z

f:Z rarrZ , f(n) ={{:((n+2)," if n is even"),((2n+1)," if n is odd" ):} State whether the function f is one - one and onto .

f: Z rarr Z, f(n)= (-1)^(n) . Find the range of f.

Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1 , "if x is even"):} is both one - one and onto .

If A=[{:(3,-4),(1,-1):}] , then prove that A^(n)=[{:(1+2n,-4n),(n,1-2n):}] where n is any positive integer .

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

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

Find the union of each of the following pairs of sets. A= {x : x = 2n+1, n in Z}, B= {x : x = 2n, n in Z}