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

Question

asked Apr 9, 2022 133k views

1 Answer

Deep Shah · Answer 1 · 2022-04-14T10:05:39+0000

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

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