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Let f(x) be periodic and k be a positive...

Let `f(x)` be periodic and `k` be a positive real number such that `f(x+k)+f(x)=0fora l lx in Rdot` Prove that `f(x)` is periodic with period `2kdot`

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To prove that the function \( f(x) \) is periodic with period \( 2k \), we start from the given condition: 1. **Given Condition**: \[ f(x + k) + f(x) = 0 \quad \text{for all } x \in \mathbb{R} \] This implies that: \[ ...
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