Question

Juliana has created the function f(x) = the quantity of 3x plus 2, divided by 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

The function is this right?
\[\Large f(x) = \frac{3x+2}{4}\]

Answer 2

I can explain the answer just help me how to find out f(x) = 3x + 2/ 4

Answer 3

Those would be really expensive text messages.

Answer 4

@jim_thompson5910 yes

Answer 5

Are you familiar with how to find the inverse of a function?

Answer 6

Somewhat

Answer 7

The basic outline is to

step 1) replace f(x) with y
step 2) swap x and y
step 3) solve for y

Answer 8

I'm stuck on solve for y part

Answer 9

\[\Large f(x) = \frac{3x+2}{4}\]
\[\Large y = \frac{3x+2}{4}\]
\[\Large x = \frac{3y+2}{4}\]
\[\Large 4x = 4*\frac{3y+2}{4}\]
\[\Large 4x = 3y+2\]
Does this help you see how to solve for y?

Answer 10

4x - 2 = 3y?

Answer 11

yes, now what comes next?

Answer 12

I'm not sure...

Answer 13

isolate the y by undoing the multiplication of 3

Answer 14

3y means 3 times y

Answer 15

what operation is the opposite of multiplication?

Answer 16

Division, I'm trying to solve it on a paper.

Answer 17

yes, so divide both sides by 3

Answer 18

4x -2 / 3 = 3y / 3?

Answer 19

\[\Large 4x-2 = 3y\]
\[\Large \frac{4x-2}{3} = \frac{3y}{3}\]
\[\Large \frac{4x-2}{3} = y\]
\[\Large y = \frac{4x-2}{3}\]
So the inverse function is
\[\Large f^{-1}(x) = \frac{4x-2}{3}\]

Answer 20

once you get the inverse function, plug in x = 24. The output will be the number of texts you can do (if you only have $24 to spend)

Answer 21

f-1(24) = 4(24) - 2 / 3?

Answer 22

yes, but make sure to use parentheis
\[\Large f^{-1}(x) = \frac{4x-2}{3}\]
\[\Large f^{-1}(24) = \frac{4*24-2}{3}\]
\[\Large f^{-1}(24) = ???\]

Answer 23

use parenthesis

instead of writing ` 4(24) - 2 / 3` write ` (4(24) - 2) / 3` instead to indicate that the "4(24)-3" portion is all over the 3

Answer 24

\[f ^{-1}(24) = \frac{ 96 }{ 3 }\]

Answer 25

you forgot about the "-2" up top

Answer 26

\[f ^{-1}(24)=\frac{ 94 }{ 3 }\]

Answer 27

what is 94/3 as a decimal?

Answer 28

31.3333333

Answer 29

that will round down to 31

so the most text messages you can send is 31. If you send 32, then you'll go over $24

Answer 30

That's the answer?

Answer 31

Well it looks like the teacher wants you to explain the whole process. Your teacher doesn't seem to be concerned with one simple numeric answer.

Answer 32

Thank you

Answer 33

you're welcome