Given a function f with the following properties. (i)f(x+h) = f(x) + e*f(h) for all real numbersx and h (ii)f(x) has a derivative for all real numbers x (iii)if prime (0) = 2 (a) Show that f(0) = 0 (b) Using the definition of f prime (0), find lim as xapproaches 0 of f(x)/x. (c) Prove there exists a real number p such that f(x) = f(x)+ pe* (d) What is the value of the number p that is describedin (c)?