Question

Problem: "A function $\inline \small f:\mathbb{N}\rightarrow \mathbb{N}$ is defined by f(1) = 1 and, for all x ≥ 1,

$\inline f(2x)=f(x)$

$\inline \small f(2x+1)=f(x)+f(x+1)$

Prove that the range of f is $\inline \mathbb{N}$ . Provide a clear proof, explaining and justifying all steps taken."

Answer 1

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