[tex]f^{-1}(x) = \sqrt[3]{\frac{x +5}{3}}\\[/tex]
Please refer to my Answer from this Questions to know more about Inverse Functions: brainly.com/question/24619467
Let [tex]y = f(x)[/tex] so that the inverse of [tex]y[/tex] is equal to [tex]f^{-1}(x)[/tex].
Solving for [tex]f^{-1}(x)[/tex]:
[tex]f(x) = 3x^3 -5 \\ y = 3x^3 -5 \\ x = 3y^3 -5 \\ 3y^3 -5 = x \\ 3y^3 = x +5 \\ y^3 = \frac{x +5}{3} \\ y = \sqrt[3]{\frac{x +5}{3}}[/tex]
Since the inverse of [tex]y[/tex] is equal to [tex]f^{-1}(x)[/tex], [tex]f^{-1}(x) = \sqrt[3]{\frac{x +5}{3}}\\[/tex].
