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

1 Answer
Jan 30, 2018

#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#