For each of the following functions, indicate the class (g(n)) the function belongs to. (Use the simplest g(n) possible in your answers.) Briefly prove your assertions.

1. 1. (n² + 1)⁵
3. 2. (10n⁴ + 7n + 3)^1/2
5. 3. 2n lg (n + 2)² + (n + 2)² lg (n/2)
7. 4. 4^n-1 + 3ⁿ⁺¹