a) The function f: x 2x 12x + 8 is defined for x R.

a) The function f: x ↦ 2x² − 12x + 8 is defined for x ∈ R.

i) Express f(x) in the form a(x + b)² + c, where a, b and care constants.

ii) Find the range of f(x).

b) The function g: x ↦ 2x² − 12x + 8 is defined for x ≥ D.

i) Find the smallest value of D for which g has an inverse.

ii) For this value of D, find an expression for g⁻¹(x) in terms of x.