I am guessing that by f sub -1 you mean the inverse of f, which is normally written here as f^-1() and in your text book as f-1(x).
f(x) =-3x+5 the inverse has to do the opposite of the function so we need to subtract 5 from x and then divide by 3 . So
f-1(x)= -1/3(x -5)
The check please:
If this is correct then f(f-1(x)) should equal x for all x in the domain of f.
So, for instance f(6)=-3(6)+5 = -18+5 = -13 and f-1(-13)= -1/3(-13-5) = -1/3(-18) = 18/3 = 6