Let `f:(0,oo)rarr R` be a (strictly) decreasing function. If `f(2a^2 + a +1)< f(3a^2-4a+1),` then the range of `a in R` is

Let f:R^(+)rarr R is a strictly decreasing function for all x in R 'such that f(k^(2)-2k)>f(3k-4) ,then k can be

Let f:[0,oo)rarr R be a continuous strictly increasing function,such that f^(3)(x)=int_(0)^(x)t*f^(2)(t)dt for every x>=0. Then value of f(6) is

Let f:R rarr R be a differentiable and strictly decreasing function such that f(0)=1 and f(1)=0. For x in R, let F(x)=int_(0)^(x)(t-2)f(t)dt

Let f:rarr R rarr(0,oo) be strictly increasing function such that lim_(x rarr oo)(f(7x))/(f(x))=1 .Then, the value of lim_(x rarr oo)[(f(5x))/(f(x))-1] is equal to

Let f:[0,oo) to R be a continuous strictly increasing function, such that f^3(x)=int_0^x tdotf^2(t)dt for every xgeq0. Then value of f(6) is_______

Let f:[0,oo) to R be a continuous strictly increasing function, such that f^3(x)=int_0^x tdotf^2(t)dt for every xgeq0. Then value of f(6) is_______

Let f:[0,oo)->R be a continuous strictly increasing function, such that f^3(x)=int_0^x t*f^2(t)dt for every xgeq0. Then value of f(6) is_______

Let f:R rarr R be a positive increasing function with lim_(x rarr oo)(f(3x))/(f(x))=1 then lim_(x rarr oo)(f(2x))/(f(x))=

Let f:R rarr R be a positive increasing function with lim_(x rarr oo)(f(3x))/(f(x))=1. Then lim_(x rarr oo)(f(2x))/(f(x))=(1)(2)/(3)(2)(3)/(2)(3)3(4)1

Show that the function f(x)=x^2 is a strictly decreasing function on (-oo,\ 0) .