Explanation:
a normal function expresses y (the functional result) in terms of x (and constants).
we need to transform this to express now x in terms of y (and constants).
at the end we only rename x into y and y into x to make it an actual function.
h(x) = y = (-5x + 6)/(3x + 4)
y(3x + 4) = (-5x + 6)
3xy + 4y = -5x + 6
4y - 6 = -5x - 3xy = x(-5 - 3y)
x = (4y - 6)/(-5 - 3y)
and after renaming we get therefore the function
y = h-1(x) = (4x - 6)/(-3x - 5)