ASSIGNMENT – Algebra

Find all functions

Find all functions f: R → R that satisfy the following conditions:

f(x) is a continuous and differentiable function throughout the domain of real numbers.

f(0) = 1 and f(1) = e (where e is the base of the natural logarithm).

f(x)f(y) = f(xy) + f(x + y) for all real numbers x and y.

f'(x) = f(x) for all real numbers x.