Answer:
[tex]f^{-1}(x)=\frac{1}{8}(x-4)^{3}[/tex]
Step-by-step explanation:
Given function is,
f(x) = [tex]\sqrt[3]{8x}+4[/tex]
To find the inverse of this function,
Rewrite the function as a equation,
y = [tex]\sqrt[3]{8x}+4[/tex]
Interchange x by y and y by x,
x = [tex]\sqrt[3]{8y}+4[/tex]
Now solve this equation for y,
x - 4 = [tex]\sqrt[3]{8y}[/tex]
(x - 4)³ = [tex](\sqrt[3]{8y})^3[/tex]
(x - 4)³ = 8y
y = [tex]\frac{1}{8}(x-4)^{3}[/tex]
Now convert the equation into function,
[tex]f^{-1}(x)=\frac{1}{8}(x-4)^{3}[/tex]
