Question

I'll give a medal again please help!!
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 equation that Juliana created is \[f(x)=\frac{ 3x+2 }{ 4 }\].
Plug in 24 for x. She wants to be able to know the amount of texts she can send with $24.
Solve the equation by dividing.

Answer 2

so it would 3x+2= 4 right?

Answer 3

So I just realized that your problem says find the inverse function.. Okay, to find the inverse of the function, you need to set f(x) into y and exchange the positions of y and x in the equation then solve for y.

\[f(x)=\frac{ 3x+2 }{ 4 }\]
would turn into
\[y=\frac{ 3x+2 }{ 4 }\]
\[x=\frac{ 3y+2 }{ 4 }\]

From here, isolate the y value.

Answer 4

By isolating the value, you need to put 3y on one side of the equation.

Answer 5

so 3y+2 over 4

Answer 6

Work from \[x=\frac{ 3y+2 }{ 4 }\] Isolate the y by multiplying both sides of the equation with 4. By multiplying both sides of the equation by 4, it will cancel out dividing the 4 on the y side.

Answer 7

After you've multiplied both sides by 4, the equation is now 4x = 3y + 2. You have to subtract 2 from both sides of the equation again to isolate y.

Answer 8

do i subtract the 2 from the y or x

Answer 9

You subtract them from both.

Answer 10

You have to get y by itself. After you've subtract 2 from both sides, 3y is still on one side of the equation. How would you get 3y to turn into y?

Answer 11

by multiply the 3y right

Answer 12

No, you divide the 3y to get 3.
Now, the equation is \[y = \frac{ 4x+2 }{ 3y }\]
That's the inverse function of the original function that Juliana created. Now, plug in 24 for x.

Answer 13

"\[x=\frac{4x-2 }{ 3 }\]"
sorry my mistake

Answer 14

Now what do i do?

Answer 15

Do you want to this in private chat?

Answer 16

Plug in 24 for x. That's the last calculation

Answer 17

so 24x-2 over 3

Answer 18

\[x=\frac{4(24)-2 }{ 3 }\]

Answer 19

ok i check that and divide it i got a decimal , is that fine?

Answer 20

You possibly can't have a decimal as the answer. Julianna can't send a half of a text.
You need to calculate the numerator first. Then, divide the numerator by the denominator.

Answer 21

i did

Answer 22

But there's still a decimal

Answer 23

Well, try to do the first part of the actual equation. What is 4 * 24?

Answer 24

ok, that is 96

Answer 25

Subtract 2 from 96.

Answer 26

-94

Answer 27

96 - 2 is 94. Divide by 3. Round your answer so that it doesn't have any decimals.

Answer 28

31

Answer 29

Correct

Answer 30

Thank you so much!!

Answer 31

did you get your medal?