# What is the inverse of f( x ) = - 6( x - 2)?

Jan 30, 2018

${f}^{-} 1 \left(x\right) = \frac{x - 12}{-} 6$

#### Explanation:

f(x) simply means a given function/ equation so don't get confused.

To start off, we multiply out the brackets...

$- 6 \times x = - 6 x$

As two negatives make a positive and $- 1 \times - 1 = 1$...

$- 6 \times - 2 = 12$

By getting rid of the previous brackets and combining terms, we get $f \left(x\right) = - 6 x + 12$.

For the inverse, simply think of it as rearranging an equation, so we want to isolate x instead of y.

We want $x$ to be on its own, so therefore we do the opposite of $12$, which is $- 12$. What we do to one side, we must do to the other. By subtracting twelve from both sides, this cancels out the $12$.

$y - 12 = - 6 x$

As we want $x$ on its own, we do not want multiple values of it. Because $- 6 x$ means $- 6 \times x$, we need to do the opposite, which is to divide by $- 6$.

$\frac{y - 12}{-} 6 = x$

As it is solved, we switch x and y to give us the answer.

${f}^{-} 1 \left(x\right) = \frac{x - 12}{-} 6$