Question

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

Answer 1

`f^(-1)(x)=(1)/(8)(x-4)^(3)`

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 =
`(1)/(8)(x-4)^(3)`

Now convert the equation into function,

`f^(-1)(x)=(1)/(8)(x-4)^(3)`