Respuesta :

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[tex]f(x)=\dfrac{19}{x^3}\to y=\dfrac{19}{x^3}\\\\\dfrac{y}{1}=\dfrac{19}{x^3}\ \ \ \ |cross\ multiply\\\\yx^3=19\ \ \ \ |:y\neq0\\\\x^3=\dfrac{19}{y}\to x=\sqrt[3]{\dfrac{19}{y}}[/tex]
Answer: [tex]f^{-1}(x)=\sqrt[3]{\dfrac{19}{x}}[/tex]