Is this a valid strong induction proof? (2 base cases)

Question

I am a university student and I was self-teaching myself induction methods.

I did question (3)(b). The answer to (3)(a) is g n = 2^n + 1 for n is a positive natural number.

My solution differs from the given solution by the university.

Mine has 2 base cases. I see that the given solution has 1 base case but it splits its inductive step into two cases (while I don't).

I've taken screenshots below for quick reference.

Question:

Given solution:

My solution (please mind my poor handwriting):

The question is, is my solution perfectly okay -i.e. is a perfectly valid strong induction proof? Is there something I have done wrong or something I have done badly against convention.

Which solution is better or preferred - and why? (i.e. which style can be more easily applied to other questions)

Thank you in advance.

Answer 1

You practically did the same thing. Your solution is completely fine.