Question

PLEASE HELP!!

Answer 1

Answer:

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

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

$f(x)=\frac{4x-3}{2}$

Part 1) Find the inverse

Let

y=f(x)

$y=\frac{4x-3}{2}$

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

$x=\frac{4y-3}{2}$

Isolate the variable y

$2x=4y-3\\4y=2x+3\\\\y=\frac{2x+3}{4}$

Let

$f^{-1}(x) =y$

so

$f^{-1}(x) =\frac{2x+3}{4}$

Part 2) we have

$f^{-1}(x) =\frac{2x+3}{4}$

where

$f^{-1}(x)$ ---->the number of weeks in the  course

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

For x=50

substitute in the inverse function

$f^{-1}(x) =\frac{2(50)+3}{4}=25.75\ weeks$

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

$50=\frac{4x-3}{2}\\\\100=4x-3\\4x=103\\x=25.75\ weeks$