Calculus help

  • Thread starter sonya
  • Start date
  • #1
sonya
23
0
calculus help please!

if f(x)= (2e^x -8)/(10e^x + 9)
then wat is f^(-1)(x)?

i first took the ln of both sides...

getting lny = ln (2e^x - 8)/(10e^x + 9)

then using one of the properties i get

lny = ln (2e^x - 8) - ln (10e^x + 9)

and from here i get stuck...how do i solve for x?? am i doing it a totally wrong way?? please help!
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
43,021
970
Pretty much, yeah, you're doing it the wrong way.

Instead of starting right off with the ln (which doesn't really help, does it?) you might want to simplfy the problem a bit first.

Since y= (2ex- 8)/(10ex+9),
(10ex+ 9)y= 2ex- 8
10exy+ 9= 2ex-8

Now subtract 9 and 2ex from both sides of the equation:
10y ex- 2ex= -17 or

(10y- 2)ex= -17

Divide both sides by 10y- 2 to isolate the exponential:

ex= -17/(10y-2)= 17/(2- 10y)

FINALLY, take the ln of both sides:

x= ln(17/(2-10y)) so the inverse function is

f-1(x)= ln(17/(2-10x)) where defined.
 
  • #3
sonya
23
0
Originally posted by HallsofIvy
Since y= (2ex- 8)/(10ex+9),
(10ex+ 9)y= 2ex- 8
10exy+ 9= 2ex-8

er...wat happened to the y? shouldn't it b 9y when u expand the y thru the brackets??
 
Last edited:
  • #4
sonya
23
0
ne1??
 
  • #5
KLscilevothma
322
0
y= (2e^x - 8)/(10e^x + 9)

(10e^x+ 9)y= 2e^x- 8

10e^xy + 9y = 2e^x - 8

10e^xy-2e^x = - (8 + 9y)

e^x = (9y + 8)/(2 - 10y)

Take ln on both sides
x = ln [(9y + 8)/(2 - 10y)]

so,
f-1(x) = ln[(9y + 8)/(2 - 10y)]

er...wat happened to the y? shouldn't it b 9y when u expand the y thru the brackets??
Yes, that should be 9y. HallsofIvy only made a careless mistake and the way I do this question is exactly the same as that of HallsofIvy.
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
43,021
970
Yes, that should be 9y. HallsofIvy only made a careless mistake

Well, yeah, I did that to see if you were paying attention.

You BELIEVE that, don't you?
 

Suggested for: Calculus help

Replies
4
Views
538
  • Last Post
Replies
8
Views
372
Replies
16
Views
450
  • Last Post
Replies
5
Views
427
  • Last Post
Replies
1
Views
236
  • Last Post
Replies
2
Views
457
  • Last Post
Replies
8
Views
348
  • Last Post
Replies
10
Views
398
  • Last Post
Replies
2
Views
339
Top