# 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.

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