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In: Advanced Math

Suppose that ?: ℝ → (0, ∞) satisfies ?(? + ?) = ?(?)?(?). Show that if...

Suppose that ?: ℝ → (0, ∞) satisfies ?(? + ?) = ?(?)?(?). Show that if ? is continuous at 0, then there is an ? ∈ (0, ∞) such that ?(?) = ?^x for all ? ∈ ℝ.

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