# Question #41170

Feb 26, 2018

$f \left(x\right) = 2 {x}^{3} - 1$

Set the function as $x = y$

$\therefore x = 2 {y}^{3} - 1$

Now rearrange for $y$.

$x + 1 = 2 {y}^{3}$

$\frac{x + 1}{2} = {y}^{3}$

$\sqrt[3]{\frac{x + 1}{2}} = y$

Now replace the $y$ with ${f}^{-} 1 \left(x\right)$

${f}^{-} 1 \left(x\right) = \sqrt[3]{\frac{x + 1}{2}}$