If `x in {1,2,3,...,9} and f_n (x) = x x x....x` (n digits) , then `f_n^2 (3)+f_n (2)`

Let f :R -{(3)/(2)}to R, f (x) = (3x+5)/(2x-3).Let f _(1) (x)=f (x), f_(n) (x)=f (f _(n-1) (x))) for pige 2, n in N, then f _(2008) (x)+ f _(2009) (x)=

Let x in(1,oo) and n be a positive integer greater than 1 . If f_n (x) =n/(1/log_2x+1/log_3x+...+1/log_nx) , then (n!)^(f_n (x)) equals to

Let f : N rarr N be defined as f(x) = 2x for all x in N , then f is

Let f(x) = (x^2 - 1)^(n+1) * (x^2 + x + 1) . Then f(x) has local extremum at x = 1 , when n is (A) n = 2 (B) n = 4 (C) n = 3 (D) n = 5

Let f (x ) = | 3 - | 2- | x- 1 |||, AA x in R be not differentiable at x _ 1 , x _ 2 , x _ 3, ….x_ n , then sum _ (i= 1 ) ^( n ) x _ i^2 equal to :

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

If f(x) = cos x\ cos 2x\ cos 2^2\ x\ cos 2^3 x\ ....cos2^(n-1) x and n gt 1, then f'(pi/2) is

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

Let f _(n) x+ f _(n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-{0}. where n in N and g (x) = max { f_(2) (x), f _(3) (x),(1)/(2)} AA x in R - {0} The number of values of x for which g(x) is non-differentiable (x in R - {0}):

If f: N to N, and x_(2) gt x_(1) implies f(x_(2)) gt f(x) AA x_(1), x_(2) in N and f(f(n))=3n AA n in N," then " f(2)= _______.