- anonymous

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.

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- anonymous

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.

- anonymous

so it would 3x+2= 4 right?

- anonymous

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.

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## More answers

- anonymous

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

- anonymous

so 3y+2 over 4

- anonymous

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.

- anonymous

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.

- anonymous

do i subtract the 2 from the y or x

- anonymous

You subtract them from both.

- anonymous

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?

- anonymous

by multiply the 3y right

- anonymous

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.

- anonymous

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

- anonymous

Now what do i do?

- anonymous

Do you want to this in private chat?

- anonymous

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

- anonymous

so 24x-2 over 3

- anonymous

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

- anonymous

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

- anonymous

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.

- anonymous

i did

- anonymous

But there's still a decimal

- anonymous

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

- anonymous

ok, that is 96

- anonymous

Subtract 2 from 96.

- anonymous

-94

- anonymous

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

- anonymous

31

- anonymous

Correct

- anonymous

Thank you so much!!

- anonymous

did you get your medal?

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