: Cadence I V I IV This cadence with inversion is correct: key Gmajor G - D/F# - G/B - C? I have a doubt with the line of bass

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Yes thats correct.

The I V I IV cadence you're showing is in the key of G(major) and holds the

I chord in root position (G - B - D)

V chord in first inversion (F# - A - D)

I chord in first inversion (B - D - G)

IV chord in root position (C - E - G)

So the bassline goes like G - F# - B - C

Slashchords are read like [Chord/Bassnote]. If the bassnote is part of the chord, you can read it as an inversion. But it could also be not part of the chord, then it can be read as the bass note which is played under the chord.

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It's possible. I wouldn't recommend it in a harmony exercise where you're required to follow the rules of SATB voice-leading though.

(Is this the WHOLE musical story, or just how guitar chords are being voiced over a separate bass instrument?)

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I assume that progression repeats...

||: G D/F# G/B C :||

...alternating I with IV and V is rock solid - all roots by fifths and fourths.

As for the bass line, the other answers point out the F# is the leading tone in G major and has the tendency to go up to G. But that isn't an absolute rule. It depends on what happens as the progression unfolds. If the bass descended by steps like G F# E D | C... the leading tone does not necessarily go back up to G. But notice that when it goes to E the line deviates from your chord progression. The leading tone in these two cases gets different treatment.

If you want to try getting your bass line to conform to the general rule about the leading tone, you could simply move it up to G and then step or jump down to the B.

It seems worthwhile to point out the sort of "musical analogy" that can happen with the leading tone and the mediant (third tone of the scale) - in your progression those the tones F# and B. Both tones are a half step below the tonic (first tone of the scale) and subdominant (fourth tone of the scale.) If you put in the bass motion F# G it mirrors the motion B C.

Those half step motions in the bass (generically I6 to IV, a first inversion chord to a root position chord with root descending by fifth) is a super important voice leading/harmony fundamental.

...I have a doubt with the line of bass

Your progression needs only that modification of F# G to fulfill that voice leading and use it in a sequential pattern. ||: G | D/F# | G G/B | C :|| with Roman numerals that contains V6 | I sequenced down a fifth to I6 | IV.

Of course you don't need to change your bass the way I'm suggesting. But you can try it and listen to the half step movements and then decide what you want to do.

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In addition to Olli's answer, depending upon what style/genre you're playing, the D/F♯ chord will want to resolve a bit differently.

The F♯ is scale-degree 7 in the key of G. It's also known as the leading tone on account of its strong tendency to resolve (or "lead up") to scale-degree 1. This tendency is especially strong when the leading tone is either the highest or lowest note. In your D/F♯ chord, this leading tone is the lowest note, so it really wants to resolve back up to G.

In other words—again, depending on the current style or genre—you would want to resolve the F♯ in the bass back up to G, so your D/F♯ chord would move to G/G instead of G/B.