[tex]f(x) = \dfrac{19}{x^3}[/tex]
Let f(x) = y:
[tex]y = \dfrac{19}{x^3}[/tex]
[tex]x^3y = 19[/tex]
[tex]x^3= \dfrac{19}{y} [/tex]
[tex]x= \sqrt[3]{\dfrac{19}{y} } [/tex]
Replacing y with x:
[tex]f^{-1}(x)= \sqrt[3]{\dfrac{19}{x} } [/tex]
[tex]\boxed { \boxed{ \text{Answer:}f^{-1}(x)= \sqrt[3]{\dfrac{19}{x} } }}[/tex]
