Question

Given: F(x) = 5x - 6 and G(x) = x - 4
F -1 =
(x + 6)/5
-6x + 10
(x + 10)/5

Answer 1

You don't need g(x) to find the inverse of f(x).  Switch the x and the y in f(x) and solve for the new y.  y = 5x -6 turns into x = 5y - 6.  Solve for y to get $y= \frac{x+6}{5}$, the first choice above.