Let f (x) be a function satisfying `f(x)=f(x)` with f(0) = 1 and g be the function satisfying `f(x) + g (x) =x^(2)`
The value of integral `int f(x) g(x) dx` is

Let f(x) be a function satisfying f\'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^2 . Then the value of integral int_0^1 f(x)g(x)dx is equal to (A) (e-2)/4 (B) (e-3)/2 (C) (e-4)/2 (D) none of these

Let f(x) be a function satisfying f'(x)=f(x) with f(0) =1 and g(x) be a function that satisfies f(x) + g(x) = x^2 . Then the value of the integral int_0^1f(x) g(x) dx , is

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Let f be a one-one function satisfying f'(x)=f(x) then (f^-1)''(x) is equal to

For x in R , the functions f(x) satisfies 2f(x)+f(1-x)=x^(2) . The value of f(4) is equal to

Let f(x) and g(x) be two functions satisfying f(x^(2))+g(4-x)=4x^(3), g(4-x)+g(x)=0 , then the value of int_(-4)^(4)f(x^(2))dx is :

Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and f(x)=1+xg(x) where underset(x to 0)lim g(x)=1 . Then f'(x) is equal to

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

If f(x) is a continuous function satisfying f(x)=f(2-x) , then the value of the integral I=int_(-3)^(3)f(1+x)ln ((2+x)/(2-x))dx is equal to