Continue to assume that the height of your cylinder is 6 inches. Write the radius r as a function of A. This is the inverse function to A(r), i. e to turn A as a function of r into. r as a function of A. To calculate an inverse function, you need to solve for r. Here you would start with A=2πr2+12πr. This equation is the same as 2πr2+12πr−A=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula.
HELP!! help solve 2πr2+12πr−A=0 using the quadratic formula and show steps

Hey, I've been jumping back and forth for the last few hours whether I should post this but in the end, I just can't find the answer to this, it's for this week's discussion board post for my class. And honestly, I have no idea where to start, it said to refer back to a previous section to get an idea of what you're supposed to do but that made me even more confused. I got 1 out of 3 questions done by looking up a tutorial but the other 2 I have no reference at all to solve it. I have 2 pages worth of notes trying to solve this but I'm not getting anywhere. I know I'm not the smartest but it's been about 4 hours now.

So a push in the right direction would be appreciated, or an example so I can see how it's done because I'm getting nowhere looking through our lessons. And it could be because I'm horrid at answering word problems that I don't understand it, but without an example, I'm not getting anywhere. All I got so far to go off to answer these are:Cylinder: (Height - 6 inches) (Surface Area - 275) (Radius - 4.26)

- Although I'm pretty sure to solve the first 2 you only need the height but could be wrong.

Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can write that as A(r). What is the domain and range of A(r)?

-I think this is (-10.26,4.26) but I can't verify the answer on the school website like the other part of the problem here.

Part b: Continue to assume that the height of your cylinder is 6 inches. Write the radius r as a function of A. This is the inverse function to A(r), i.e. r as a function of A or r(A). What is r(A) and what is the domain and range of r(A)? What is r(A)?

r(A)=

-I have no idea how to tackle this part, it gave this equation to "help me":

"A(r) = 2πr^2+2πrh = 2πr^2+12πr"

As it suggests I tried this on a calculator and it gave me:

"A= 2π(r+6)"

I'm pretty sure I'm supposed to do something else with that information but I wouldn't know where to start, I'm going to take a break from this and try again later because it's been stressing me out.

(this one I can verify if it's the right answer or not on the webpage!)

Any help is appreciated nonetheless!

both equations and proportions are better.