Let `f` be a function such that `f(x).f\'(-x)=f(-x).f\'(x)` for all `x` and `f(0)=3`. Now answer the question:`int_-51^51dx/(3+f(x))=` (A) `34` (B) `102` (C) `0` (D) `17`

Let f be a function such that f(x).f\'(-x)=f(-x).f\'(x) for all x and f(0)=3 . Now answer the question:The value of f(x)f(-x) for all x is (A) 9 (B) 4 (C) 16 (D) 12

Let f be a function such that f(x).f\'(-x)=f(-x).f\'(x) for all x and f(0)=3 . Now answer the question:Number of roots of equation f(x)=0 in interval [-2,2] is (A) 0 (B) 2 (C) 4 (D) 1

Let f be a polynomial function such that f(3x)=f'(x);f''(x), for all x in R. Then : .Then :

Let f be a function such that f(3)=1 and f(3x)=x+f(3x-3) for all x. Then find the value of f(300).

Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)

Let f(x) be a function such that f'((1)/(x))+x^(3)f'(x)=0. What is int_(-1)^(1)f(x)dx

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

If function f satisfies the relation f(x)*f'(-x)=f(-x)*f'(x) for all x and f(0)=3, and if f(3)=3, then the value of f(-3) is

Let f:R rarr R be a function such that f(2-x)=f(2+x) and f(4-x)=f(4+x), for all x in R and int_(0)^(2)f(x)dx=5. Then the value of int_(10)^(50)f(x)dx is

Let f(x) be a function such that,f(0)=f'(0)=0,f''(x)=sec^(4)x+4 then the function is