1 Answer

Hal Eisen · Answer 1 · 2022-12-21T02:19:21+0000

Answer:

$f^(-1)(x) = \sqrt[3]{(x -4)/(5)} +2$

Explanation:

Given

f(x) = 5(x - 2)^3 + 4

Required

Determine the inverse

f(x) = 5(x - 2)^3 + 4

Replace f(x) with y

y = 5(x - 2)^3 + 4

Swap the positions of x and y

x = 5(y - 2)^3 + 4

Make y the subject

x -4= 5(y - 2)^3

Divide by 5

(x -4)/(5)= (y - 2)^3

Take cube roots of both sides

$\sqrt[3]{(x -4)/(5)}= y - 2$

Add 2 to both sides

$\sqrt[3]{(x -4)/(5)} +2 = y$

$y = \sqrt[3]{(x -4)/(5)} +2$

Replace y with
f^(-1)(x)

$f^(-1)(x) = \sqrt[3]{(x -4)/(5)} +2$

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