If a function satisfies the relation `f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1,` then
The value of `underset(x to -oo)(lim)f(x)` is

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

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

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))

f(x)= x^(2)-3x + 4 If f(x)= f(2x+1) find the value of x .

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)= 2 , then (a)f(x) must be polynominal function(b)f(3)=12 (c)f(0)=0 (d)f(x) may not be differentiable

If 2f (x)- 3f((1)/(x))= x^(2) (x ne 0) then f(2)= ……

If f'(x)=x^(2)+5 and f(0)=-1 then f(x)=...

A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

A function y = f(x) satisfies the condition f(x+(1)/x) =x^(2)+1/(x^2)(x ne 0) then f(x) = ........