If `f:NrarrN 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 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.

Evaluate (n!)/((n-r)!) , when n = 6, r = 2

Let f:Wto 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.

A function f from the set of natural numbers N to the set of integers Z is defined by f(n)={((n-1)/(2),"when n is odd"),(-(n)/(2),"when n is even"):} Then f(n) is -

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

Let f(x)=(x-1)^4(x-2)^n ,n in Ndot Then f(x) has (a) a maximum at x=1 if n is odd (b) a maximum at x=1 if n is even (c) a minimum at x=1 if n is even (d) a minima at x=2 if n is even

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

let NN be the set of natural numbers and f: NN uu {0} rarr NN uu [0] be definedby : f(n)={(n+1 " when n is even" ),(n-1" when n is odd " ):} Show that ,f is a bijective mapping . Also that f^(-1)=f

The sum of first n terms of the series 1^(2)+ 2 . 2^(2) + 3^(2) + 2. 4 ^(2) + 5^(2) +… is n/2 (n+1) ^(2) when n is even , When n is odd then the sum will be-

Prove that ((-1+sqrt(-3))/(2))^(n)+((-1-sqrt(-3))/(2))^(n) =2, when n is positive integer multipel of 3, =-1 when n is positive integer but not a multiple of 3.