1. ## I NEED HELP. THEYRE NOT TOO BAD.

hey need some quick help. my friend and i are trying to figure these out but cant seem to do it. i was waiting for replies from earleir, but no such luck:

find the rule of inverse of the function f(x)=(4x+2)/(x-4) and i know you make sure it passes the vertical line test, then replace the x's with y's and see if they equal one another and theyre supposed to, i guess, but we keep getting y+2. is this right?

then, we have to find the rule of inverse for f(x)=(the square root of)x+2 which i can't even do on my own because i'm not sure if it's asking me to do what i did in the problem before.

last, i have a rectangle thats 22x29 inches and the corners are cut off so that it can be folded into a box without a top. i have to find the opposite lengths of the sides of the removed squares if the volume is no more than 1000 cubic centimeters. i know that i have to use the equation v=x(22-2x)(29-2x), but i want to be sure. help with it?

thanks guys.

2. Originally Posted by amandarporter
find the rule of inverse of the function f(x)=(4x+2)/(x-4) and i know you make sure it passes the vertical line test, then replace the x's with y's and see if they equal one another and theyre supposed to, i guess, but we keep getting y+2. is this right?
thanks guys.
First step: replace x with y and y with x.

So you get $\displaystyle x = \frac{4y + 2}{y - 4}$.

Now multiply both sides by $\displaystyle y - 4$:

$\displaystyle x(y - 4) = 4y + 2$

Simplify:

$\displaystyle xy - 4x = 4y + 2$

$\displaystyle xy - 4x - 2 = 4y$

$\displaystyle -4x - 2 = 4y - xy$

$\displaystyle -4x - 2 = (4 - x)y$

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

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