Exercise 7, j. : With G sharp as the soprano note, write in four parts a triad in first inversion, with the subdominant of G sharp minor in the bass. It seemed to me that such a chord does not exist. The book does not have answers to its exercises. Edit: Added a photo of the page!
The subdominant of G♯ minor is C♯ minor. The C♯ minor chord is C♯-E-G♯. The first inversion of that chord is E-G♯-C♯. So that would mean that E should be the bass note.
But the question is a bit badly worded in that it asks you to put the subdominant of G♯ minor in the bass which could make you think that C♯ should be in the bass. But then it would be root position and not first inversion.
As I understand it, the exercise simply asks for a first inversion chord with a C sharp in the bass (and a G sharp in the soprano). That would be an A sharp half diminished seventh chord (we have four voices so let’s put the seventh in). The second degree also has subdominant function in case you’re worried about that, but to be annoyingly exact the exercise doesn’t specify the function of the chord, just the bass note. I am certain the usage of the word “subdominant” does not indicate the function of the chord since the exercise specified that the subdominant should be put in the bass. A function is a property of the complete harmony, not of a single voice (in fact, in most cases it is trivial to construct multiple chords with various functions on the same note), so this cannot be the intended meaning.
The underlying problem is that the exercise uses the word “subdominant” to mean the fourth note of the scale. I’ve encountered this usage quite frequently and in my opinion, it is a terrible idea. Tonic, subdominant and dominant are harmonic functions, so if you use the same words for specific notes it can only lead to confusion (of which your question is proof). Additionally, consider this: if “dominant” can, in addition to a harmonic function, denote just the fifth note of the scale, the seventh degree would be a dominant-function chord without the note named dominant. Conversely, using this hair-brained naming scheme you could say that the subdominant is the seventh of the dominant chord. Besides, it is completely unnecessary to have the function names also denote specific notes, there is nothing wrong with just using the number in the scale. (For example “the fourth [note of the scale]”, the part brackets only added if context demands explicit distinction.)