Question

Help Consider function f. F(x) = ^3square8x + 4

Answer 1

Answer:

$f^{-1}(x)=\frac{1}{8}(x-4)^{3}$

Step-by-step explanation:

Given function is,

f(x) = $\sqrt[3]{8x}+4$

To find the inverse of this function,

Rewrite the function as a equation,

y = $\sqrt[3]{8x}+4$

Interchange x by y and y by x,

x = $\sqrt[3]{8y}+4$

Now solve this equation for y,

x - 4 = $\sqrt[3]{8y}$

(x - 4)³ = $(\sqrt[3]{8y})^3$

(x - 4)³ = 8y

y = $\frac{1}{8}(x-4)^{3}$

Now convert the equation into function,

$f^{-1}(x)=\frac{1}{8}(x-4)^{3}$