Answer:
[tex]f^{-1}(x)=6(x+7)^{3}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt[3]{\frac{x}{6}}-7[/tex]
Let
[tex]y=f(x)\\ y=\sqrt[3]{\frac{x}{6}}-7[/tex]
Exchanges the variable x for y and y for x
[tex]x=\sqrt[3]{\frac{y}{6}}-7[/tex]
Isolate the variable y
[tex]x+7=\sqrt[3]{\frac{y}{6}}[/tex]
elevates to the cube both members
[tex](x+7)^{3}=\frac{y}{6} \\ \\y=6(x+7)^{3}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=6(x+7)^{3}[/tex] ------> inverse function
