Answer:
f^(-1)(x) = -3x/(3x-3)
Explanation:
1) replace f(x) by y
● y = 3x/(5x+3)
2) exchange x and y
● y = 3x/(5x+3)
● x = 3y / (3y +3)
3) solve for y
● x = 3y / (3y +3)
● x (3y +3) = 3y
● 3xy + 3x = 3y
● 3xy - 3y = -3x
● y (3x - 3) = -3x
● y = -3x /(3x-3)
4) replace y with f^(-1)(x)
● y = -3x/(3x-3)
● f^(-1)(x) = -3x/(3x-3)