# 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.