Question

Let f(x) = 2x - 6. Solve f-1(x) when x = 2.

Okay... so we need the inverse of x.
So f(x) can just be set to y... right?
y = 2x - 6
2x = y - 6
x = y - 3
2 = y - 3
y = -5?

Or is this completely wrong?

Answer 1

y = 2x - 6
` 2x = y - 6` mistake
x = y - 3
2 = y - 3
y = -5?

Answer 2

-2x = -y - 6?

Answer 3

Because I added the first time, so would I need to subtract instead?

Answer 4

yes

y = 2x - 6

to isolate x, first step is to add 6 both sides :
y + 6 = 2x

next, divide 2 both sides :
(y+6)/2 = x

Answer 5

now you can switch x and y :
(x+6)/2 = y

Answer 6

so the inverse function is :
\[\large y = (x+6)/2\]

Answer 7

plugin x = 2

Answer 8

So then 2 + 6/2 which is just 8/2 = 4

Answer 9

So lets do a practice one to make sure I got it right

Let f(x) = 2x + 2. Solve f-1(x) when x = 4.

y = 2x + 2
y - 2 = 2x
(y - 2/2) = x

Plug in 4.

4 - 2 /2 = x
x = 1

Answer 10

thats right ! but don't forget about parenthesis

Answer 11

Let f(x) = 2x + 2. Solve f-1(x) when x = 4.

y = 2x + 2
y - 2 = 2x
`(y - 2/2) = x` your teacher cries at this step

Plug in 4.

4 - 2 /2 = x
x = 1

Answer 12

Corrected below :

Let f(x) = 2x + 2. Solve f-1(x) when x = 4.

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

Plug in 4.

`(4 - 2) /2 = x`
x = 1

Answer 13

Techy wechy. Thanks!

Answer 14

yw!