Question

I need help with this, it’s from my practice prep guide

Answer 1

`g(x)\text{ = }\frac{\sqrt[3]{12x-12}}{2}`

Step-by-step explanation:

Here, we want to get the inverse of the function f(x) which is represented as g(x)

We start by replacing f(x) by y and making x the subject of the formula

We proceed as follows:

`\begin{gathered} y\text{ = }(2)/(3)x^3+\text{ 1} \\ \text{ multiply through by 3} \\ 3y=2x^3\text{ + 3} \\ 3y-3=2x^3 \\ x^3\text{ = }(3y-3)/(2) \\ x\text{ = }\sqrt[3]{(3y-3)/(2)} \\ \\ g(x)\text{ = }\sqrt[3]{(4(3x-3))/(2*4)} \\ \\ g(x)\text{ = }\frac{\sqrt[3]{12x-12}}{2} \end{gathered}`