If `f: N rarr Z` is defined by `f(n) ={{:((n-1)/(2),"when n is odd"),(-n/2,"when n is even"):}` then identify the type of function

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 State whether the function f is bijective. Justify yur answer.

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.

Let f:WrarrW 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.

Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-one but not onto.

In each of the following cases,state whether the function is onto,one to one or bijective.Justify your answer if:NrarrN defined by f(n)={((n+1)/2,n is odd),(n/2,n is even):}

Let i= sqrt-1 . If a sequence of complex numbers is defined by z_(1)=0, z_(n+1)= z_(n)^(2)+i for n ge 1 , then find the value of z_(111) .

Let A = {9,10,11,12,13} and let f : A rarr N be defined by f (n) = the highest prime factor of n. find the range of f.

Let N rarr R be a function defined as f(x) = 4x^2 + 12x +15 Show that f : N rarr S , where, S is the range of f, is invertible. Find the inverse of f.

Evaluate (n !)/((r )!(n-r) !) , when n=5, r =2