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 defined0 by: f(n)={(n+1)/2, if n is odd (n-1)/2, if n is even Show that f is a bijection.

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

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

check that f : N- N defined by f(n)={(n+1)/2,(if n is odd)),(n/2,(if n is even)) is one -one onto function ?

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 }

If n gt 0 is an odd integer and x = (sqrt(2) + 1)^(n), f = x - [x], " then" (1 - f^(2))/(f) is

Let f : N->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 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 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 . Prove that f is many-one, onto function.

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)