Hi!
Okay, so -
We are going to replace f(x) with the variable y.
So, f(x) = 2x - 6 is now equal to y = 2x - 6.
Now, we are going to swap the variables. Where we once had x, we will now have y. And where we once had y, we will now have x.
So y = 2x - 6 is now equal to x = 2y - 6.
Now, we need to isolate y on one side of the equation. We must do this by getting rid of the -6, and the 2 multiplied by the variable y.
We get rid of these values by doing the inverse of their operation. Since 6 is negative, we will add it to itself in order for it to cancel out. But, when we do something on one side of the equation - we must do it on the other.
So, we will add 6 on both sides.
x + 6 = 2y - 6 + 6.
x + 6 = 2y.
Okay, now - we cannot add x to 6, because they are unlike terms. So, what we do next <span>instead is divide both sides by 2. Remember, we're doing the inverse of the operation. The inverse of multiplication is division, so we will divide both sides by 2.
</span>

= 2y / 2.

= y.
Now, we change the y into

, and we have our inverse.

=

.
Hopefully, this helps! =)