# How do you find the inverse function f(x) = -3 x^7-2?

Jul 18, 2015

Let $y = f \left(x\right)$ and apply a sequence of operations to both sides of the equation to isolate $x$ and find:

${f}^{- 1} \left(y\right) = - \sqrt[7]{\frac{y + 2}{3}}$

#### Explanation:

Let $y = f \left(x\right) = - 3 {x}^{7} - 2$

Add $2$ to both ends to get:

$y + 2 = - 3 {x}^{7}$

Divide both sides by $- 3$ to get:

${x}^{7} = - \frac{y + 2}{3}$

Take $7$th root to get:

$x = \sqrt[7]{- \frac{y + 2}{3}} = - \sqrt[7]{\frac{y + 2}{3}}$ (since ${\left(- 1\right)}^{7} = - 1$)

So ${f}^{- 1} \left(y\right) = - \sqrt[7]{\frac{y + 2}{3}}$