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

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 }

Find the 18^("th") and 25^("th") terms of the sequence defined by a_(n)={{:(n(n+2)",","if n is even natural number"),((4n)/(n^(2)+1)",","if n is odd natural number"):}

Let N be the set of 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) . Then, fog is

Let N be the set of 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) . Then, fog is (A) one-one but not onto (B) onto but not one-one (C) both one-one and onto (D) neither one-one nor onto

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 f be function f:N to N be defined by f(x)=3x+2, xin N . Find the images of 1, 2, 3

Prove that ((n + 1)/(2))^(n) gt n!

If f:NrarrZ f(n)={(n-1)/2; when n is odd =-n/2; when n is even Identify the type of function