anonymous
  • 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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • 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
  • anonymous
so it would 3x+2= 4 right?
anonymous
  • 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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anonymous
  • anonymous
By isolating the value, you need to put 3y on one side of the equation.
anonymous
  • anonymous
so 3y+2 over 4
anonymous
  • 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
  • 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
  • anonymous
do i subtract the 2 from the y or x
anonymous
  • anonymous
You subtract them from both.
anonymous
  • 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
  • anonymous
by multiply the 3y right
anonymous
  • 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
  • anonymous
"\[x=\frac{4x-2 }{ 3 }\]" sorry my mistake
anonymous
  • anonymous
Now what do i do?
anonymous
  • anonymous
Do you want to this in private chat?
anonymous
  • anonymous
Plug in 24 for x. That's the last calculation
anonymous
  • anonymous
so 24x-2 over 3
anonymous
  • anonymous
\[x=\frac{4(24)-2 }{ 3 }\]
anonymous
  • anonymous
ok i check that and divide it i got a decimal , is that fine?
anonymous
  • 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
  • anonymous
i did
anonymous
  • anonymous
But there's still a decimal
anonymous
  • anonymous
Well, try to do the first part of the actual equation. What is 4 * 24?
anonymous
  • anonymous
ok, that is 96
anonymous
  • anonymous
Subtract 2 from 96.
anonymous
  • anonymous
-94
anonymous
  • anonymous
96 - 2 is 94. Divide by 3. Round your answer so that it doesn't have any decimals.
anonymous
  • anonymous
31
anonymous
  • anonymous
Correct
anonymous
  • anonymous
Thank you so much!!
anonymous
  • anonymous
did you get your medal?

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