Let a function `f(x)` be such that `f"(x)=f'(x)+e^(x)&f(0)=0,f'(0)=1` then find the value of `ln(((f(2))^(2))/(4))`

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)

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

Let f(x) be a function such that f''(x) = f'(x) + e^x and f'(0) =1 , f(0) = 0 then (1) ln((f(2))^2/4)=4 (2) Range of f(x) is [-1/e,oo) (3) for xgt-2 , tangent at any point of f(x) lies below the curve (4) for x<-1 f(x) is decreasing function

Let f:(-2,2)rarr(-2,2) be a continuous function such that f(x)=f(x^(2))AA in d_(f), and f(0)=(1)/(2), then the value of 4f((1)/(4)) is equal to

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

Let f:W rarr W be a given function satisfying f(x)=f(x-1)+f(x-2) for x<=2. If f(0)=0 and f(1)=1, ther find the value of f(2)+f(3)+f(4)+f(5)+f(6)

[" Let "f(x)" be a function such that "],[f''(x)=f(x)" and "f'(0)=f(0)=0" .The "],[" value of "(f(x))/(4-f(x))dx" is equal to "]

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

If f(x) be a differentiable function,such that f(x)f(y)+2=f(x)+f(y)+f(xy);f'(0)=0,f'(1)=2 then find f(x)