[" If "f(n)=(9n^(2)+b)^(3)" then find the "],[" function of Such that "f(g(n))=g(f(n))]

If f_(n)(x),g_(n)(x),h_(n)(x),n=1, 2, 3 are polynomials in x such that f_(n)(a)=g_(n)(a)=h_(n)(a),n=1,2,3 and F(x)=|{:(f_(1)(x),f_(2)(x),f_(3)(x)),(g_(1)(x),g_(2)(x),g_(3)(x)),(h_(1)(x),h_(2)(x),h_(3)(x)):}| . Then, F' (a) is equal to

The function f: N to N defined by f(n) =2n+3 is

f: N rarr N , f(n) = (n+5)^(2) , n in N , then the function f is ............

Leg g(x)=ln(f(x)), whre f(x) is a twice differentiable positive function on (0,oo) such that f(x+1)=xf(x) .Then,for N=1,2,3,......g^(n)(N+(1)/(2))-g^(n)((1)/(2))=

If f(alpha)=f(beta) and n in N , then the value of int_alpha^beta (g(f(x)))^n g\'(f(x))*f\'(x)dx= (A) 1 (B) 0 (C) (beta^(n+1)-alpha^(n+1))/(n+1) (D) none of these

If f(alpha)=f(beta) and n in N , then the value of int_alpha^beta (g(f(x)))^n g\'(f(x))*f\'(x)dx= (A) 1 (B) 0 (C) (beta^(n+1)-alpha^(n+1))/(n+1) (D) none of these

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

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 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 }