Question

Find the inverse of:
h(x) = 5(x-9)^(3)

Answer 1

\[\Large h(x) = 5(x-9)^{3}\]


\[\Large y = 5(x-9)^{3}\]


\[\Large x = 5(y-9)^{3}\]


\[\Large \frac{x}{5} = (y-9)^{3}\]


\[\Large \sqrt[3]{\frac{x}{5}} = y-9\]


\[\Large \sqrt[3]{\frac{x}{5}}+9 = y\]


\[\Large y=\sqrt[3]{\frac{x}{5}}+9\]


So the inverse function is \[\Large h^{-1}(x)=\sqrt[3]{\frac{x}{5}}+9\]