Need help with the following question please:

9. (5) Let f(n)2 I there anything wrong with the following proof by induction that f(n) O(n)? Basis: The case n 1 is trivially satisfied since f(1) 1 is a constant. Induction Hypothesis: Assume that f(n - 1)Sc(n-1) for some constant c >0 Induction step: n2 (n-1)2 +2n-1 f(n-1 ) + 2n-1 c(n-1) +2n-1 (c + 2)n-c-1 f(n) = = S = (c+2)n Therefore by definition of the big O, f(n)-O(n)