$\backslash$table$[[\backslash$table$[[$Algorithms and Data Structures$],[$Final Exam$]],$Spring $2024]]$

Question $1(10$ points$)$: Give short but formal proofs of the following:

$($a$)f(n)=6n-{10}^{14}$ is $O(n),$ but $f(n)=2^{2n-2}$ is not $O(2^n)$

$($b$)f(n)=O(g(n)),$ where $f(n)=19n+15$ and $g(n)=n^2-50n.$