Question

Inverse of a function

Answer 1

I already know the answer, I just want to understand it

Answer 2

Well the first thing we do to make this easier is replace f(x) with y.

Answer 3

And then you switch x and y.

Answer 4

Right, got it :)

Answer 5

\[y = 12 - \frac{ 3 }{ 4 }x~---> x = 12 - \frac{ 3 }{ 4 }y\]

Answer 6

And then you solve for y to isolate it again.

Answer 7

That's where I'm stuck, I'm not sure where to start

Answer 8

Well here we want to get rid of the fraction because who doesn't hate fractions. The denominator is 4 so we multiply both sides by 4.

Answer 9

\[x \times 4 = 12 - \frac{ 3 }{ 4 }y \times 4\]

Answer 10

So I have 4x = 12 - 3y?

Answer 11

We are multiply the entire side by 4, so the 4 will apply to ALL terms. the 4x is correct and so is the 3y, but we apply it to the 12 as well.

Answer 12

Okay, wasn't sure about that, alright, one sec, let me write it down

Answer 13

np

Answer 14

Alright so we have 4x = 48 - 3y so now we do what?

Answer 15

We move more terms. We can remove the 3 on the y. 3y is being multipled so we divide 3 on both sides.

Answer 16

Ack, hold on. The frist thing we had to do was subtract 12 on both sides. Woops.

x = 12 - 3/4y
x - 12 = -(3/4)y
4(x - 12) = -3y

Answer 17

I thought that was going in the wrong direction lol. no worries

Answer 18

So do you understand so far? Just to make sure since I made a mistake there. :x

Answer 19

Yes, I got it so far :)

Answer 20

So now we divide both sides by 3, correct?

Answer 21

Alright.

4(x - 12) = -3y

Now we can pass on the -3. We divide it on both sides.

Answer 22

Yes. =)

Answer 23

Sweet, you got me to the right answer. I appreciate it :)

Answer 24

It would be -4/3(x - 12)

If you want to avoid confusion you can just multiply the inverse.

From (-3/4)y you can change it to -4/3 and attach it to the x. SAme exact thing, less confusion. Dividing a fraction is the same and multiply by its inverse!

Answer 25

Np, also make sure that you use \[f^{-1}(x)\] to replace the y we changed at the beginning

Answer 26

to indicate :)

Answer 27

Right, I'm just practicing stuff so I can get better at math, thanks again for helping so much :)