Let `f : R -> [4,oo)` be an onto quadratic function whose leading coefficient is1, such that `f'(x)+f'(2-x)=0` Then the value of, `int_1^3 (dx)/(f(x))` is equal to

Let f:R rarr[4,oo) be an onto quadratic function whose leading coefficient is 1, such that f'(x)+f'(2-x)=0 Then the value of,int_(1)^(3)(dx)/(f(x)) is equal to

Let f: R rarr R be a function such that f(2)=4 and f'(2)=1 . Then, the value of lim_(x rarr 2) (x^(2)f(2)-4f(x))/(x-2) is equal to

Let f(x) be a non-negative continuous function defined on R such that f(x)+f(x+1/2)=3 , then the value of 1/1008 int_(0) ^(2015) f(x) dx is

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral int_(0)^(a) (1)/(1+e^(f(x)))dx is equal to

Let f(x) be a non-negative continuous function defined on R such that f(x)+ f(x+(1)/(2))=3 ,then the value of (1)/(1008)*int_(0)^(2016)f(x)dx

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:R rarr R be a continuous function and f(x)=f(2x) is true AA x in R .If f(1)=3 then the value of int_(-1)^(1)f(f(x))dx is equal to (a)6(b) 0 (c) 3f(3)( d) 2f(0)

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

Let f(x) be a real valued function such that f(x)=f((121)/(x)),AA x>0. If int_(1)^(11)(f(x))/(x)dx=5, then the value of int_(1)^(121)(f(x))/(x)dx is equal to

Let f :R to [(3)/(4), oo) be a surjective quadratic function with line of symmetry 2x -1=0 and f (1) =1 int (e ^(x))/(f (e ^(x)))dx