To find the inverse, look at the fcn as y = (5x-2)/(3x) and exchange the x and y to get
x = (5y-2)/(3y) and solve for y:
=> 3xy = 5y-2
=> 3xy-5y = -2
=> y(3x-5) = -2
=> y = (-2)/(3x-5) is your inverse fcn
Plug a couple values into one and send the results through the inverse to make sure it checks out.