Question

Can somebody help me with 12 and 13 ? I don’t know how to find the inverse for those functions

Answer 1

12) To answer this question, we will set the equation y=f(x), solve for x, and then exchange x and y.

Setting y=f(x) we get:

`y=9+2\sqrt[3]{x}.`

Subtracting 9 from the above equation we get:

`\begin{gathered} y-9=9+2\sqrt[3]{x}-9, \\ y-9=2\sqrt[3]{x}. \end{gathered}`

Dividing the above equation by 2 we get:

`\begin{gathered} (y-9)/(2)=\frac{2\sqrt[3]{x}}{2}, \\ (y-9)/(2)=\sqrt[3]{x}. \end{gathered}`

Taking the above equation to the power of 3 we get:

`\begin{gathered} ((y-9)/(2))^3=(\sqrt[3]{x})^3, \\ ((y-9)/(2))^3=x. \end{gathered}`

Exchanging x and y we get:

`((x-9)/(2))^3=y.`

Therefore:

`f^(-1)(x)=((x-9)/(2))^3.`

Answer:

`f^(-1)(x)=((x-9)/(2))^3.`