\(Let y = (2x − 3)³ − 8.\)

To find the inverse, solve for x in terms of y:

\((2x − 3)³ = y + 8\)

\(2x − 3 = \sqrt[3]{y + 8}\)

\(2x = \sqrt[3]{y + 8} + 3\)

\(x = \frac{\sqrt[3]{y + 8} + 3}{2}\)

\(Thus, f⁻¹(x) = \frac{\sqrt[3]{x + 8} + 3}{2}.\)

The range of f is the domain of f⁻¹. Calculate the range of f for 2 ≤ x ≤ 4:

\(For x = 2, f(2) = (2(2) − 3)³ − 8 = −7.\)

\(For x = 4, f(4) = (2(4) − 3)³ − 8 = 117.\)

Therefore, the domain of f⁻¹ is −7 ≤ x ≤ 117.