[tex]f(x) = \frac{19}{x^3}[/tex]
Set f(x) = y and solve for x:
[tex]y = \frac{19}{x^3}[/tex]
[tex]\frac{19}{y} = x^3[/tex]
[tex]x = \sqrt[3]{\frac{19}{y} }[/tex]
Now, switch the x and y:
[tex]y = \sqrt[3]{\frac{19}{x} }[/tex]
Now, write it in the correct notation, and your answer is:
[tex]f^{-1}(x) = \sqrt[3]{\frac{19}{x} }[/tex]
Hope I could help!
