Question

If f(x)=2x-6, then f^-1(x)=

Answer 1

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 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.


`(x + 6)/(2)` = 2y / 2.


`(x + 6)/(2)` = y.

Now, we change the y into
`f^(-1)(x)`, and we have our inverse.


`f^(-1)(x)` =
`(x + 6)/(2)`.

Hopefully, this helps! =)

Answer 2

f(x) = 2x - 6

y = 2x - 6

Switching y and x and solving for y;

x = 2y - 6

2y = x + 6

y =
`(x+6)/(2)`

Hence,


`f^(-1) = (x+6)/(2)`