Suppose y = L(x) = ax + b (with a ≠ 0) is the equation of the line tangent to the graph of a one-to-one function f at (x₀, y₀). Also, suppose that y = M(x) = cx + d is the equation of the line tangent to the graph of f^-1 at (y₀, x₀).

a. Express a and b in terms of x₀ and y₀.

b. Express c in terms of a, and d in terms of a, x₀, and y₀.

c. Prove that L^-1 (x) = M(x).