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Grace [21]
4 years ago
12

PLEASE HELP!!

Mathematics
1 answer:
e-lub [12.9K]4 years ago
6 0

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

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