To solve for the inverse of a function, you have to interchange the variables x and y and solve for the value of y in terms of x:
F(x) = 5x/3 + 5
y = 5x/3 + 5
Interchange x and y:
x = 5y/3 + 5
Solve for the value of y in terms of x:
x – 5 = 5y/3
5y = 3 (x – 5)
y = 3 (x -5) / 5
f^-1 (x) = 3 (x -5) / 5