Question

what is the inverse function for f(x)=[tex] \frac{19}{x^3}

Answer 1

$f(x) = \dfrac{19}{x^3}$

Let f(x) = y:
$y = \dfrac{19}{x^3}$
$x^3y = 19$
$x^3= \dfrac{19}{y}$
$x= \sqrt[3]{\dfrac{19}{y} }$

Replacing y with x:
$f^{-1}(x)= \sqrt[3]{\dfrac{19}{x} }$

$\boxed { \boxed{ \text{Answer:}f^{-1}(x)= \sqrt[3]{\dfrac{19}{x} } }}$