Inverse Functions. Test Prep help.

[Seiya]

hey lads, i just was wondering if i solved this right:

5. Consider the function f(x) = 3x+cos(x), defined on the interval [0, pi]

(a) prove that f has an inverse function g. Note: you are note expected to find the inverse function g indicate your reasoning.

I dre the graph of f(x) and showed its a one to one function with a horizontal line test... I am not sure this is enough please tell me if i have to do anything extra

then i said that any continuos 1 to 1 function has a inverse function with the change of domain and range...

(b) determine the domain and range of the funcion g

since the function domain was A and range B, the inverse domain is B and range A.

function = d [0,pi] r [1,8.421]
inverse = d[1,8.4] r [0,pi]


(c) determine the derivative g'(3pi/2) Hint: first, show that f(xo) = 3(pi/2) when x0 = pi/2

find the derivative of the function at xo then the derivative of the inverse is 1/derivativefunction

is all my reasoning right? I am sure illl have this on my final, any advice appreciated

 

[opticaltempest]

Hello,

Being that this was a good review problem for me, I went ahead and worked it through on video. I only worked part (a). This video is about 12MB so it might take a few minutes if your on dial-up. I hope this helps you out.

http://www.zippyvideos.com/5562444952738986/monotonic_function_12-18-05/*deriveit"

 

[Seiya]

hmm i guess you did the same thing as me just with much more detail ;) alright ill show as much detail on my test, thanks for the vid! how did u make it anyway really nice lol

 

[opticaltempest]

I have a quickcam 4000 which is focused on a piece of paper, at a distace of about 6 inches. Using logitech's included software, I record the .avi file. Once the .AVI is recored, if you have Windows XP it is very simple to use Windows Media Encoder or Windows Movie Maker to convert it to .WMV format. From there, just upload it to a free video hosting site such as putfile.com or zippyvideos.com. It's much to easier recording myself writing and talking than it is typing each step and converting all the equations to latex. I hope others will do this :)