f(x) = [tex]4\sqrt[3]{x} - 8[/tex]
Let's replace f(x) with y
y = [tex]4\sqrt[3]{x} - 8[/tex]
Switch the x and y
x = [tex]4\sqrt[3]{y} - 8[/tex]
Now, let's solve for y. Start off by adding 8 to both sides.
x + 8 = [tex]4\sqrt[3]{y}[/tex]
Divide both sides by 4
[tex]\frac{x}{4} + 2[/tex] = [tex]\sqrt[3]{y}[/tex]
Take each side by the power of 3
[tex](\frac{x}{4} + 2)^{3}[/tex] = y
Now, let's replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)[/tex] = [tex](\frac{x}{4} + 2)^{3}[/tex] is the inverse
