![f(x)=\sqrt[]{(x+4)/(3)}](https://img.qammunity.org/2023/formulas/mathematics/college/3xb6koanyvi715bwkjmmmd598bd2xlvmwe.png)
To find the inverse do these steps
1- Put f(x) = y
2- Switch x and y
3- solve to find the new y
Let us do that
![y=\sqrt[]{(x+4)/(3)}](https://img.qammunity.org/2023/formulas/mathematics/college/vv1gbrnw9oxia5p9aw06r8wvfnql0c5bia.png)
Switch x and y
![x=\sqrt[]{(y+4)/(3)}](https://img.qammunity.org/2023/formulas/mathematics/college/yb7dnflo6wc7s48htyeze73ywljinvgwg2.png)
Now square the two sides to cancel the root

Multiply both sides by 3 to cancel the denominator

Subtract 4 from both sides

The rule is the answer D