# Iterative Nightmare

Calculus Level 1

Let $$f,g : \mathbb{R} \longrightarrow \mathbb{R}$$ such that $$f(2x)=2f(x)$$ and $$g(x) = x+ f\bigg(x+f\Big(\, x+f\big(\, x+f(\cdots)\, \big)\, \Big)\bigg).$$

Is it always true that $$g(2x)=2g(x)?$$

Note: $$f$$ and $$g$$ are not necessarily continuous over $$\mathbb{R}.$$

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