A finction ` f: R-> R` has property `f(x+y)=f(x)* e^((f(y)-1)`, for every `x,y in R` then positive value of `f(4)` is

A finction f:R rarr R has property f(x+y)=f(x)*e^((f(y)-1)), for every x,y in R then positive value of f(4) is

If f(x + y) = f(x) - f(y), forall x, y in R , then show that f(3) = f(1)

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

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

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

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 _______