Find the inverse of each of the following functions by first switching x and y and then solving for yy = ( (1)/(4)x + 6) ^(3)

Question

find the inverse of each of the following functions by first switching x and y and then solving for y
`y = ( (1)/(4)x + 6) ^(3)`

Answer 1

`y\text{ = 4(}\sqrt[3]{x}\text{ - 6)}`Step-by-step explanation:
`y=((1)/(4)x+6)^3`

First we switch x and y:

`x\text{ = (}(1)/(4)y+6)^3`

Then we would solve for y:

`\begin{gathered} \text{cube root both sides:} \\ \sqrt[3]{x}\text{ = }\sqrt[3]{((1)/(4)}y+6)^3 \\ \sqrt[3]{x}\text{ = }(1)/(4)y+6 \\ \end{gathered}`
`\begin{gathered} \sqrt[3]{x}\text{ -6= }(1)/(4)y \\ \sqrt[3]{x}\text{ -6 = }(y)/(4) \\ 4(\sqrt[3]{x}\text{ -6) = y} \end{gathered}`
`y\text{ = 4(}\sqrt[3]{x}\text{ - 6)}`