The function f is defined by f(x) = 4x² − 24x + 11, for x ∈ ℝ.

i. Express f(x) in the form a(x − b)² + c and hence state the coordinates of the vertex of the graph of y = f(x). The function g is defined by g(x) = 4x² − 24x + 11, for x ≤ 1.

ii. State the range of g.

iii. Find an expression for g⁻¹(x) and state the domain of g⁻¹.