Question

What is the inverse of the function f(x)= 19/x^3 ?

Answer 1

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