Question

Juliana has created the function f(x) = 3x+2 over 4 to represent the cost of texting on her current plan, where x represents the number of texts. Juliana discovers that, using the inverse function to solve for x = 24, she can predict how many texts she can use for $24. Explain to Juliana how to accomplish this, using complete sentences.

Answer 1

Magic is the way. e.e

Answer 2

really?

Answer 3

Ofc Ofc

Answer 4

@Shadow

Answer 5

Do you know how to get the inverse of a function?

Answer 6

sorta im not strong at it no but i can try

Answer 7

Well you know it or you don't. Do you know the first step to getting the inverse of a function?

Answer 8

First, replace f(x) with y

Answer 9

then switch the x and y's

Answer 10

Yes.

f(x) and y are interchangeable. f(x) stands for the function of x. So y is the function of x. You don't need to switch them but it makes your life easier.

Then you switch the positions of x and y. Then you solve for the variable that you switched to the right side.

So it would go like:
\[f(x) = \frac{ 3x + 2 }{ 4 }\]
\[y = \frac{ 3x + 2 }{ 4 } \]
\[x = \frac{ 3y + 2 }{ 4 } \]
\[4x = 3y + 2\]
\[4x - 2 = 3y \]
\[\frac{ 4x - 2 }{ 3} = y \]
Cosmetic change, cause this is how we usually visualize equations.
\[y = \frac{ 4x - 2 }{ 3 }\]

Answer 11

ok showing Juliana the equation is explaining to her how to accomplish it?

Answer 12

Well they want it in words, 'complete sentences.' I expressed that in my above response.

Answer 13

so i would write down

Juliana in order to accomplish your goal the first thing you need to do is take f(x) and change it to y because f(x) and y are interchangeable. Next we talk x and y and switch them so 3x would turn into 3y and instead of y= it would be x=. Doing it this way makes life easier. Then you solve for the variable that you switched to the right side.

Answer 14

^is that correct

Answer 15

I think your lesson has a typo. x represents the # of texts, yet they note $24 as being a value for x. I am sure they mean y.

Answer 16

Try to use your own words, not mine. Teachers can usually tell when you copy and paste as they have plenty of samples of your work.

Answer 17

So you would put 24 in for a value of y, as we found the inverse function and isolated y. Then you can solve for the number of texts that you can send with $24.

Answer 18

the only thing of yours i used was "f(x) and y are interchangeable." and "Then you solve for the variable that you switched to the right side." thats it the other 90% is my own words

Answer 19

wait you just confused me alittle bit what do you mean

Answer 20

were do we add the 24?

Answer 21

Okay, let's go back to the beginning. What are we trying to do?

Answer 22

first we switch f(x) with y then switch y with X

Answer 23

Okay that's the first step of obtaining the inverse function. But why do they want us to do that?

Answer 24

they want us to inverse because it makes the equation easier to solve?

Answer 25

Anime I am giving you my time to help you understand. I could easily type out the answer and you'd get an A but you would never learn and would likely fail any tests. If you don't want to be present for my help, that's okay. I have an essay to write. But I'd appreciate if you stayed out of chat when I'm waiting for a response from you.

Answer 26

Is that fair?

Answer 27

what are you talking about shadow im giving my time to its not like i wanna be here im waiting on your responses so i talk in the chat i see you doing the same thing during helping people it not my fault i didnt reply that exact moment you press post

Answer 28

That's because I already have stuff posted for them to go through and respond to.

Answer 29

Im doing my best to learn this as fast as i can and give the answers im suppose to give just give me a break this is difficult for me im not genius like you people

Answer 30

I already understand this material.

Answer 31

Lets move on. Read the question again. Why are they having you do all this math? What do they want you to solve for?

Answer 32

The latter question is a hint.

Answer 33

they want me to solve for the amount of text that can be sent with only $24

Answer 34

Correct. So what do x and y represent?

Answer 35

the amount of text being sent

Answer 36

and the money being used for it

Answer 37

x is the first or second one

Answer 38

first x= amount of text
y= Amount of money

Answer 39

Correct. So does that answer your question of where you should add the 24?

Answer 40

Juliana in order to accomplish your goal the first thing you need to do is take f(x) and change it to y because f(x) and y are interchangeable. Next we take x and y and switch them so 3x would turn into 3y and instead of y= it would be x=. Doing it this way makes life easier. You also need to remember x= the amount of text being sent and y= the amount of money you can spend. Then you solve for the variable that you switched to the right side.

Answer 41

^good?

Answer 42

Sure. Just know that the practice of verbatim (repeating someone else's words) in note taking or homework doesn't instill concepts as strongly. When you take their words and put it into your own, you remember it better. If you'd like I could show you the study, but the disparity in test scores is massive when it comes to conceptual questions.

But sure, that works.

Answer 43

i used 2 things you said not the whole thing 90% is my words

Answer 44

So after you solve for the variable on the right side, what do you get/have to do?

Answer 45

simplify?

Answer 46

So we are at
\[y = \frac{ 4x - 2 }{ 3 } \]

Input 24 in for y, solve for x.

You get the # of texts you can send with $24

Answer 47

ummmmmmmmmmm

so 24=4x-2 over 3

Answer 48

Yes

Answer 49

switch the sides \[\frac{ 4x-2 }{ 3 }=24\]

Answer 50

Then...............Multiply by 3 on both sides? \[\frac{ 3(4x-2) }{ 3 }=24 \times3\]

Answer 51

Mhm

Answer 52

PEMDAS

Answer 53

Shadow don't mean to interrupt could you help me after this question ?

Answer 54

thennnnnn..............4x-2 which = 2?

Answer 55

right

Answer 56

Add two to both sides, then divide by 3.

Answer 57

Don't know what 4x-2 which = 2 means

Answer 58

PEMDAS () first so (4x-2) so i put 4x-2 = 2

Answer 59

How does 4x - 2 = 2

Answer 60

I dont know i was just thinking 4-2=2 which would make it 3*2 over 3

Answer 61

x = 1

Answer 62

does it = 1/2

Answer 63

Okay so you are correct that you do parentheses first when it comes to PEMDAS but you can't do anything with (4x -2).
\[y = \frac{ 4x - 2 }{ 3 }\]
You want to substitute 24 in for y so we can get the # of texts we can send with $24.
\[24 = \frac{ 4x - 2 }{ 3 }\]
Multiply both sides by 3
\[72 = 4x - 2\]
Add two to both sides
\[74 = 4x \]
Divide both sides by 4
\[x = 18.5\]
What do you think the correct answer is?

Answer 64

18.5 text per 24 dollars she spends

Answer 65

You can't send half a text

Answer 66

18.5 dollars for the text she sends monthly

Answer 67

What variable did we just solve for

Answer 68

x

Answer 69

Which is the # of texts you can send in a month

Answer 70

texts messages I SAID THAT BUT U SAID U CANT SEND A HALF A MESSAGE

Answer 71

Yeah but you can send 18

Answer 72

ok i got it i think thx shadow i have a few more but help mike out

Answer 73

Hes been patiently waiting

Answer 74

mhm