Answer
Find when he will have 30 assignments completed for the inverse function.
To prove
As given
Pedro has created the function.
[tex]f(x) = \frac{4x -3}{2}[/tex]
Where x represents the number of weeks in the course .
Pedro discovers that using the inverse function to solve for x = 30.
he can predict when he will have 30 assignments completed.
Now find the inverse of the function f(x) .
[tex]Take\ y = f(x) = \frac{4x -3}{2}[/tex]
[tex]2y + 3 = 4x [/tex]
[tex]x = \frac{2y + 3}{4}[/tex]
Now change the y variable into x. (Because this is inverse function of f(x)).
Thus
[tex](f(x))^{-1} = \frac{2x + 3}{4}[/tex]
Thus this is the inverse function of f(x).
Put x = 30
[tex](f(x))^{-1} = \frac{2\times 30 + 3}{4}[/tex]
[tex](f(x))^{-1} = \frac{60 + 3}{4}[/tex]
[tex](f(x))^{-1} = \frac{63}{4}[/tex]
[tex]Therefore\ in\ \frac{63}{4}\ weeks\ Pedro\ completed\ 30\ assignment.[/tex]
In mixed fraction form
[tex]Therefore\ in\ 15 \frac{3}{4}\ weeks\ Pedro\ completed\ 30\ assignment.[/tex]
