If `f:{1,2,3....}->{0,+-1,+-2...}` is defined by `f(n)={n/2, if n ` is even , ` -((n-1)/2) if n ` is odd `}` then `f^(-1)(-100)` is

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Number of ways in which three numbers in A.P. can be selected from 1,2,3,..., n is a. ((n-1)/2)^2 if n is even b. n(n-2)/4 if n is even c. (n-1)^2/4 if n is odd d. none of these

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 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 }

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

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.

Let f(n)=2cosn xAAn in N , then f(1)f(n+1)-f(n) is equal to

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

If f(n+1)=1/2{f(n)+9/(f(n))},n in N , and f(n)>0 for all n in N , then find lim_(n->oo)f(n)

Let N be the set of natural numbers and two functions f and g be defined as f, g : N to N such that : f(n)={((n+1)/(2),"if n is odd"),((n)/(2),"if n is even"):}and g(n)=n-(-1)^(n) . The fog is :