angelamaebrooke
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PLEASE HELP!!
Juliana has created the function f(x) = 4x - 3 / 2 to represent the number of assignments he has completed, where x represents the number of weeks in the
course. Juniana discovers that, using the inverse function to solve for x = 50, she can predict when she will have 50 assignments completed. Explain to
Juliana how to find the inverse and find when she will have the 50 assignments completed, using complete sentences.

Respuesta :

calculista

Answer:

Part 1) The inverse function is [tex]f^{-1}(x) =\frac{2x-3}{4}[/tex]

Part 2) 25.75 weeks

Step-by-step explanation:

Let

x ---->the number of weeks in the  course

f(x) ---> the number of assignments he has completed

we have

[tex]f(x)=\frac{4x-3}{2}[/tex]

Part 1) Find the inverse

Let

y=f(x)

[tex]y=\frac{4x-3}{2}[/tex]

Exchange the variables (x for y and y for x)

[tex]x=\frac{4y-3}{2}[/tex]

Isolate the variable y

[tex]2x=4y-3\\4y=2x+3\\\\y=\frac{2x+3}{4}[/tex]

Let

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

so

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

Part 2) we have

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

where

[tex]f^{-1}(x)[/tex] ---->the number of weeks in the  course

x ---> the number of assignments he has completed

For x=50

substitute in the inverse function

[tex]f^{-1}(x) =\frac{2(50)+3}{4}=25.75\ weeks[/tex]

Note: Juliana don't need to use the inverse function. you can just use the function you have where f(x)=50 assignments and solve for x to get the amount of weeks.

so

[tex]50=\frac{4x-3}{2}\\\\100=4x-3\\4x=103\\x=25.75\ weeks[/tex]

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