Question

find the inverse of each of the following functions by first switching x and y and then solving for y$y = ( \frac{1}{4}x + 6) ^{3}$

Answer 1

$y\text{ = 4(}\sqrt[3]{x}\text{ - 6)}$Explanation:$y=(\frac{1}{4}x+6)^3$

First we switch x and y:

$x\text{ = (}\frac{1}{4}y+6)^3$

Then we would solve for y:

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