# Find the inverse of the function f(x)= -5x How would I do this?

Dec 27, 2017

${f}^{-} 1 \left(x\right) = - \frac{x}{5}$

#### Explanation:

Replace $f \left(x\right)$ with $y$

$y = - 5 x$

Replace $y$ with $x$ and vice versa:

$x = - 5 y$

Solve for $y$:

$- \frac{x}{5} = y$ (Divide by $- 5$ to isolate $y$)

$y = - \frac{x}{5}$ (Rewrite so that $y$ is the subject of the equation)

$\therefore {f}^{-} 1 \left(x\right) = - \frac{x}{5}$