Answer:
Option B
[tex]\red{ \boxed{ \bold{ {f}^{ - 1} (x) = \sqrt[3]{ - x - 9} }}}[/tex]
Step-by-step explanation:
[tex]f(x) = - {x}^{3} - 9 \\ plug \: f(x) = y \\ \implies \: y = - {x}^{3} - 9 \\ interchange \: x \: and \: y \\ \\ x = - {y}^{3} - 9 \\ \\ x + 9 = - {y}^{3} \\ \\ - x - 9 = {y}^{3} \\ \\ \sqrt[3]{ - x - 9} = y \\ \\ \sqrt[3]{ - x - 9} = {f}^{ - 1} (x) \\ \\ \red{ \boxed{ \bold{ {f}^{ - 1} (x) = \sqrt[3]{ - x - 9} }}}[/tex]
