Let `f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0` and f(0)=0 then the value of `f(1) +f(2)=`

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then find the value of f(7)dot

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))dot

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))dot

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to

An even polynomial function f(x) satisfies a relation f(2x)(1-f(1/(2x)))+f(16x^2y)=f(-2)-f(4x y)AAx ,y in R-{0}a n df(4)=-255 ,f(0)=1. Then the value of |(f(2)+1)//2| is_________

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7 , then the value of int_(1)^(4)f'(x)dx is

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______