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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

Respuesta :

calculista

Let

x-------> the number of texts

f(x)------> the cost of texting on Juliana's current plan

we know that

[tex] f(x) = (3x+2)/4 [/tex]

Step [tex] 1 [/tex]

Find the inverse function of f(x)

[tex] f(x) = (3x+2)/4 [/tex]

Let

y=f(x)

[tex] y = (3x+2)/4 [/tex]

exchange the variables x for y and  y for x

[tex] x = (3y+2)/4 [/tex]

Clear variable y

[tex]x= (3y+2)/4\\ 4x= 3y+2\\ 3y=4x-2\\ y=(4x-2)/3[/tex]

Let

[tex] f(x)^{-1}=y [/tex]

[tex] f(x)^{-1}=(4x-2)/3 [/tex] ------> this is the inverse function

where

x ------> represent the cost

f(x)^{-1}------> the number of texts

Solve for [tex] x=\$24[/tex]

substitute

[tex] f(x)^{-1}=(4x-2)/3 [/tex]

[tex] f(x)^{-1}=(4*24-2)/3 [/tex]

[tex] f(x)^{-1}=31.33 [/tex]

therefore

the answer is

[tex] 31\ texts[/tex]

hlarson2016

Answer:

31 texts

Step-by-step explanation:

X=the text and f(x)=the cost. First, she needs to find the inverse of her function. The function is  f(x) 3x+2/4. We will let y=f(x). Substitute f(x) with y. Now we have y= 3x+2/4. Then we flip the variables in the equation so x for y and y for x. Then we have, x=3y+2/4. Next, we want to clear for variable y. 4x+3y=2, 3y=4x-2, and y=(4x-2)/3. Next, let f(x)^-1=y. Then we plug in what y equals (which we already solved). The inverse function is, f(x)^-1=4x-2/3. Next, we have to solve for x=$24. All we do to solve is substitution. f(x)^-1=4(24)-2/3, and then f(x)^-1=31.33. The answer would come out to 31 total texts.

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