Inverse Problem (1 Viewer)

[conics2008]

I need help with the last part of this inverse question.

F(x) = 1/1+e^-x

i) show f(x) has no stationary points
ii) Describe the behaviour of f(x) as a) postive direction b) negative direction without limit.
iii) sketch y=f(x)
iv) explain why f(x) has invesrse and sketch both on the same axes.
vi) show f^-1(1/2)= 0 and f^-1(5/6) = ln5
vii) hence evaluate S from 5/6 to 1/2 f^-1(x) dx

vii) is annoying me.. i integrated the orginal function F(x) from 5/6 and 0 but thats wrong answer ??

can u help me out please thanks.

 

[cwag]

did you subtract that answer from the area of the rectangle [(5/6 -1/2) * f(5/6)] to find the integral for inverse function?

 

[conics2008]

cwag yeah .. the rectangle yeap i forgot it makes it alot easier.. thanks =]

i know these type of question always use the dam rectangle xD

thans

 

[conics2008]

did you subtract that answer from the area of the rectangle [(5/6 -1/2) * f(5/6)] to find the integral for inverse function?

hey its actually 5/6 * ln5/6 - ln 3

thanks btw..

 

[cwag]

oh your right...sorry..mind was wondering

 

[conics2008]

but u reminded me of the stupid shapes invovled to make the quetion alot easier soo credit to you xD

 

[u-borat]

say what's happening?

with the last part, isn't it the rectangle 5/6 X Ln5?
And then you minus the integral from 0 to Ln5 of the original function?

Or am i wrong? =S

 

[conics2008]

say what's happening?

with the last part, isn't it the rectangle 5/6 X Ln5?
And then you minus the integral from 0 to Ln5 of the original function?

Or am i wrong? =S

yeap thats the same method i did but forgot to minus the rectangle.

 

[u-borat]

as in, are those numbers right?
just checking.