Investigating Functions

Algebra Level 3

Let \(f(x) \) be a periodic function and \(g(x) \) be a non-periodic function, which of the following statement(s) is/are true?

Statement 1: \( f(g(x)) \) will be periodic.
Statement 2: \( g(f(x)) \) will be periodic.
Statement 3: Both \(f(g(x))\) and \( g(f(x)) \) maybe periodic.
Statement 4: All the statements above are true.