Pedro has created the function f(x) = the quantity of 4x minus 3, divided by 2 to represent the number of assignments he has completed, 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. Explain to Pedro how to accomplish this, using complete sentences.

Question

anonymous · Answer

$$4x - 3 \over 2$$

rsadhvika · Answer

Since $\large  f(x) = \frac{4x-3}{2}$  tells you # of assignments Pedro completes, given the week number,
its inverse function should tell him how many weeks it should take to complete 30 assignments.

rsadhvika · Answer

Start by finding the inverse function of $f(x)$

anonymous · Answer

so were looking for f(-1)?

rsadhvika · Answer

yup, we're looking for $f^{-1}(x)$

anonymous · Answer

is this the equation where we input -1 for x?

rsadhvika · Answer

Nope, 
first we need to find the inverse funciton :-


$\large  f(x) =y  = \frac{4x-3}{2}$

$\large  y = \frac{4x-3}{2}$

multiply 2 both sides

$\large  2y = 4x-3$

add 3 both sides

$\large  2y+3 = 4x$

divide 4 both sides

$\large  \frac{2y+3 }{4}= x$

switch x, y

$\large  \frac{2x+3 }{4}= y$

rsadhvika · Answer

thats the inverse function of f(x)

anonymous · Answer

Oh ok, thats when you switch x and y

rsadhvika · Answer

put x = 30 in this function, 
it will tell u how many weeks it takes to complete 30 assignments :-

$\large  \frac{2x+3 }{4}= y$

put x = 30

$\large  \frac{2(30)+3 }{4}= y$

$\large  \frac{60+3 }{4}= y$

$\large  \frac{63 }{4}= y$

$\large  15.75 = y$


so it wud take 16 weeks to complete 30 assignments !

rsadhvika · Answer

see if that makes some sense

anonymous · Answer

I think I got it

anonymous · Answer

Gimme a sec to write it down :)

rsadhvika · Answer

okie

anonymous · Answer

got it, thanks :)