Question

if f(x)=3x+3, then f^-1(x)=?

Answer 1

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and y where x is.
Solve for y
Replace y with f^-1(x)

Answer 2

Huh?

Answer 3

Those are the steps for solving the inverse

Answer 4

Okay

Answer 5

So lets go over this step by step, what does it say we should do first

Answer 6

Replace f(x) with the y

Answer 7

Yes, so \[y = 3x+3\] next?

Answer 8

Switch the x's and y's

Answer 9

Right interchange them

Answer 10

wouldn't it be 3x+3 still?

Answer 11

\[x=3y+3\]

Answer 12

Now simply solve for y

Answer 13

Okay how so? I don't understand how

Answer 14

We need to use algebra, remember how I mentioned how important it is :P

Ok so since we are solving for y, lets first get rid of the +3 on the right side, what would we do?

Answer 15

subtract 3 from both sides

Answer 16

Exactly

Answer 17

\[x-3=3y\] now we need to get rid of that 3 being multiplied to the y, how can we move it?

Answer 18

divide by 3?

Answer 19

Right!

Answer 20

\[y = \frac{ x-3 }{ 3 } = \frac{ x }{ 3 }-1\]

Answer 21

Good?

Answer 22

yeah

Answer 23

Ok now last step is to replace y with f^(-1)

Answer 24

And behold we have our inverse!

Answer 25

Okay so can you help me set it up?

Answer 26

and sorry if i'm keeping you up its late

Answer 27

It's done, that's our answer \[y= \frac{ x }{ 3 }-1 \implies f^{-1}(x) = \frac{ x }{ 3 }-1\]

Answer 28

okay

Answer 29

thanks bud

Answer 30

I'm done for the night have a good one

Answer 31

Yw :), take care

Answer 32

Here is a video on explaining what exactly this means, I recommend you watch it: https://www.khanacademy.org/math/algebra2/manipulating-functions/introduction-to-inverses-of-functions/v/introduction-to-function-inverses