About A/F — uncommon voicings
A/F is F, A, C# and E — with F put in the bass.
It sounds like the major triad it is, resting on a different floor. If F is already one of the chord’s notes this is an inversion, and if it is not it is a new colour under an unchanged chord; either way the reason to reach for it is a bass line that walks by step where root-position chords would leap.
Inversion or pedal — the harmony is unchanged; only the bass moves.
Also written A over F or A with F in the bass.
What these less common shapes are
What to play over A/F
Read A/F as a maj7♯5 -- the lydian augmented chord, which puts it in F lydian augmented.
Each of those is a page: the scale across the neck, and the chords it harmonises into — which is where A/F sits in it. Every scale.
Chords near A/F
Change one note of A/F and you have (drop the flat thirteenth), (the flat thirteenth becomes the major seventh), (the fifth becomes the major seventh), (the flat thirteenth becomes the ninth), (the flat thirteenth becomes the sixth) or (the flat thirteenth becomes the flat seventh).
A/F is a slash chord — a triad over a named bass note. Slash chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.