Question

Juliana has created the function f(x)=3x+2/4 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

@Gerardo_cast23 @Falco276 @Hero

Answer 2

Is it

\[f(x) = \frac{3x + 2}{4}\] or \[f(x) = 3x + \frac{2}{4}\]

Answer 3

the first one!

Answer 4

What's interesting is, you actually have to find the inverse of the function.

Answer 5

I suppose that's what you're having trouble with, right?

Answer 6

YES exactly

Answer 7

To find the inverse of the function, you're supposed to change \(f(x)\) to \(y\), swap \(x\) and \(y\), then isolate y afterwards.

Answer 8

So you have

\[f(x) = \frac{3x + 2}{4}\]

Changing \(f(x)\) to \(y\) you get:
\[y = \frac{3x + 2}{4}\]

Swapping \(x\) and \(y\) you get:
\[x = \frac{3y + 2}{4}\]

Can you isolate \(y\) from here?

Answer 9

thats where I have the problemm

Answer 10

To finish,

1. Multiply 4 on both sides
2. Subtract 2 on both sides
3. Divide both sides by 3

Answer 11

i dont get where u multiply the 4 on the fraction side

Answer 12

\[4 \dot\ x = \frac{3y + 2}{4} \dot\ 4\]\[4 \dot\ x = \frac{3y + 2}{\cancel{4}} \dot\ \cancel{4}\]\[4x = 3y + 2\]

Answer 13

y = 4x-2 / 3

Answer 14

Lastly you have to replace \(y\) with \(f^{-1}(x)\)

Answer 15

f -1 (x) = y= 4x-2 /3

Answer 16

Now, that you have inversed the function, the domain and range are the inverse of what they were before.

Answer 17

Thank you! Can u help with another pleasE?

Answer 18

oh but now my answer..do i sub 24?

Answer 19

I was just about to ask you about that

Answer 20

You have to find \(f^{-1}(24)\)

Answer 21

So 4(24) -2 / 3?

Answer 22

@Hero

Answer 23

Yes, what did you get?

Answer 24

31.3

Answer 25

Well, we should say approximately 31 texts for $24

Answer 26

Since it is not possible to send .3 texts.

Answer 27

lol yeah ok so 31 texts she can send

Answer 28

Correct.

Answer 29

To check, input f(31) into the original function to see if you get 24.

Answer 30

Ok . please help me understand this one

Answer 31

Marrie is logging the number of radioactive isotope she observes every minute. She has determined her function to be f(x) =-4x +120. Based on the situatuion above describe and neccesary restrictions to the domain and range

Answer 32

I've answered this kind of question already. You should scroll through my questions answered to find it.

Answer 33

okkay !

Answer 34

u have way too many lol

Answer 35

Thank you @broskishelleh

Answer 36

@Hero You're a saint! Thanks for clearing that up!