The function f is defined for p ≤ x ≤ q, where p and q are positive constants, by f : x ↦ x² − 2x − 15.

The range of f is given by c ≤ f(x) ≤ d, where c and d are constants.

i. Express x² − 2x − 15 in the form (x + a)² + b.

ii. State the smallest possible value of c. For the case where c = 9 and d = 65,

iii. Find p and q,

iv. Find an expression for f⁻¹(x).