Question

Find the inverse of the function. f(x) = the cube root of quantity x divided by eight. - 4

Answer 1

`\bf f(x)=y=\sqrt[3]{\cfrac{x}{8}}-4\impliedby \textit{first, let's switch the variables about} \\\\\\ \underline{x}=\sqrt[3]{\cfrac{\underline{y}}{8}}-4\implies x+4=\sqrt[3]{\cfrac{\underline{y}}{8}}\implies (x+4)^3=\cfrac{y}{8} \\\\\\ \boxed{8(x+4)^3=y}\impliedby f^(-1)(x)`

Answer 2

`f^(-1)(x)=8(x+4)^(3)`

Explanation:

we have

`f(x)=\sqrt[3]{(x)/(8)}-4`

Let

`y=f(x)`

`y=\sqrt[3]{(x)/(8)}-4`

Exchanges the variable x for y and y for x

`x=\sqrt[3]{(y)/(8)}-4`

Isolate the variable y

`x+4=\sqrt[3]{(y)/(8)}`

elevates to the cube both members

`(x+4)^(3)=(y)/(8) \\ \\y=8(x+4)^(3)`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=8(x+4)^(3)` ------> inverse function