In: Advanced Math
Suppose that ?: ℝ → (0, ∞) satisfies ?(? + ?) = ?(?)?(?). Show that if ? is continuous at 0, then there is an ? ∈ (0, ∞) such that ?(?) = ?^x for all ? ∈ ℝ.
A detailed solution is provided below
For any quarries let me know, otherwise hope it helps:-)
Please upvote if it helps.