If `f(x)` satisfies the equation `|(f(x-2), f(x+5), f(x-2)), (5,4,-5), (10,12,30)| = 0 AA x in RR` Then the value of `f(2009)` is equal to

If a function f(x) satisfies the relation 3f(x)-5f((2)/(x))=3-x+x^(2)AA x in R-{0} ,then the value of f(1) is equal to

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x,AA x in R Then find the value of f(0)

A continuous function f:RRrarrRR satisfies relation f(x)+f(2x+y)+5xy=f(3x-y)+2x^(2)+1" for all "x,y in RR, then the value of |f(4)| is equal to -

The function f(x) satisfying the equation f^(2)(x)+4f'(x)f(x)+(f'(x))^(2)=0

The function f(x) satisfying the equation (f (x))^2 + 4 f'(x) f(x) + (f'(x))^2 = 0

The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (f'(x))^2 = 0

Let f(x) be a function which satisfies the relation f(x+1)+f(2x+2)+f(1-x)+f(2+x)=x+1 AA x in R then value of [f(0)] is

If f(x) = (x - 1)(x - 2)(x - 3)(x - 4)(x - 5) , then the value of f' (5) is equal to

If f(x) = (x - 1)(x - 2)(x - 3)(x - 4)(x - 5) , then the value of f' (5) is equal to

" Let "f(x)" be a function which satisfies the relation "f(x+1)+f(2x+2)+f(1-x)+f(2+x)=x+1AA x in R" then value of "[f(0)|" is "