Answer: [tex]f^{-1}(x) = \sqrt[3]{\frac{x+6}{(-2)} }[/tex]
The inverse of f is a function
Step-by-step explanation:
[tex]f(x) = -2x^{3}-6\\f^{-1}(x) = y = -2x^{3}-6\\y + 6 = -2x^{3}\\\frac{y+6}{-2} = x^{3}\\x = \sqrt[3]{\frac{y+6}{(-2)} } \\f^{-1}(y) = \sqrt[3]{\frac{y+6}{(-2)} } \\So, f^{-1}(x) = \sqrt[3]{\frac{x+6}{(-2)} }[/tex]
The inverse of f is a function since every single x only has 1 answer for y
