Question

find the inverse function of $f(x)=9 + sqrt3{x}$. $f^{-1}(x)=$

Explanation:

Step1: Replace $f(x)$ with $y$

$y = 9+\sqrt[3]{x}$

Step2: Swap $x$ and $y$

$x = 9+\sqrt[3]{y}$

Step3: Solve for $y$

First, subtract 9 from both sides: $x - 9=\sqrt[3]{y}$. Then cube both sides: $(x - 9)^3=y$.

Answer:

$(x - 9)^3$