Let f be a function from the set of positive integers to the set of real number i.e `f : N rarr R`, such that `f(1) + 2f{2} + 3f{3} + ….. + nf{n} = n(n + 1) f(n)` for `n ge 2`
Then the of `1/f(4)` must be

Let f be a function from the set of positive integers to the set of real number i.e f : N rarr R , such that f(1) = 1 and r=1 to n ∑ ​ rf(r)=n(n+1)f(n),∀n≥2' then the value of 2126f(1063)

Let R be the set of all real numbers f:RrarrR be given by f(x)=3x^2+1 .Then the set f^(-1) , (1,6) is

If f(x) = (p - x^n)^(1/n), p gt 0 and n is positive integer, then the value of f[f(x)]

If f:R rarr R be defined by f(x)=x^2+3 where R is the set of real numbers then show that f^(-1)(7)={-2,2} and f^(-1)(19)={-4,4}

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

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 -

A mappin f : N rarrN where N is the set of natural numbers is defined as f(n)=n^(2) for n odd f(n)=2n+1 for n even for n inN . Then f is

A function f from the set of natural numbers to the set of integers defined by f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d; -n/2,\ w h e n\ n\ i s\ e v e n (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

Let n be a positive integer with f(n)=1!+2!+3!+….+n! and P(x) and Q(x) be polynomials in x such that f(n+2) = Q(n)f(n) + P(n)f(n+1) . Find P(2).

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 :