this is my first time making a post on this website so all feedback is highly appreciated.
I have recently started university and I struggle a bit with wording answers as I am not use to it yet. If anyone could take a quick look at my workings and wording to this question it would be much obliged.
If anything is wrong with how I have formatted the answer or any lines are incorrect please do not hesitate to mention it.
That's fine. It can be done more compactly; the following would be completely acceptable as a proof.
We show that $f(g(1)) \not = 1$ (from which it follows that $f$ is not inverse to $g$, since $f$ is defined to be inverse to $g$ if $f(g(x)) = x$ for all $x$, and $g(f(x)) = x$ for all $x$). Indeed, $g(1) = 3$, and $f(3) = 269$, so $f(g(1)) = 269$.