Problem #PRU-109997

Problems Calculus Functions of one variable. Continuity Certain properties of a function and recurrence relations. Continuous functions (general properties)
 15–16  4.0

Problem

On a function f(x) defined on the whole line of real numbers, it is known that for any a>1 the function f(x) + f(ax) is continuous on the whole line. Prove that f(x) is also continuous on the whole line.