Question

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

Answer 1

`f^-1(x)=(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 xx x=-6x`

As two negatives make a positive and `-1 xx -1 =1`...

`-6 xx -2=12`

By getting rid of the previous brackets and combining terms, we get `f(x)=-6x+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=-6x`

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

`(y-12)/-6 =x`

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

`f^-1(x)=(x-12)/-6`