Consider functions f satisfying the following four conditions:
(1) f is real-valued and defined for all real numbers.
(2) For any two real numbers x and y we have f(xy)=f(x)f(y).
(3) For any two real numbers x and y we have f(x+y)≤2(f(x)+f(y)).
(4) We have f(2)=4.Prove that:
a) There is a function f with f(3)=9 satisfying the four conditions.
b) For any function f satisfying the four conditions, we have f(3)≤9. functionalgebraalgebra proposedfunctional equationFunctional inequalityfunctional inequalities