Question

Let f(x) =

`\sqrt[3]{11x - 3 \:} determine \: {f}^( - 1) (x)`? here ​

Answer 1

Explanation:

Set up f(x).

`\sqrt[3]{11x - 3} = f(x)`

Replace f(x) with y

`\sqrt[3]{11x - 3} = y`

Swap x and y

`\sqrt[3]{11y - 3} = x`

Solve for y

Cube both sides

`11y - 3 = {x}^(3)`

Add 3 to both sides

`11y = {x}^(3) + 3`

Divide both sides by 11

`y = \frac{x {}^(3) + 3 }{11}`

so

`f {}^( - 1) (x )= \frac{ {x}^(3) + 3}{11}`