The x intercept of f-1(x) is the y intercept of f(x). The y intercept of f-1(x) is the x intercept of f(x). A horizontal asymptote for f(x) produces a vertical asymptote for f-1(x). A vertical asymptote for f(x) produces a horizontal asymptote for f-1(x).
(2 1/2, 0)
f(x) = 2 1/2 - 3 1/3 * x
or
f(x) = 5/2 - (10/3)*x
f^-1(x) is the inverse of f(x), which is obtained replacing f(x) by x, and x by y, and solving for y, as follows:
x = 5/2 - (10/3)*y
(10/3)*y = 5/2 - x
y = (5/2)*(3/10) - x*(3/10)
y = (3/4) - (3/10)*x
f^-1(x) = (3/4) - (3/10)*x
at x-intercept, f^-1(x) = 0,
(3/4) - (3/10)*x = 0
(3/4) = (3/10)*x
x = (3/4)*(10/3)
x = 5/2 or 2 1/2