Sum1 here help

  • Thread starter sonya
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  • #1
sonya
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sum1 here help!

ok...since no1s helpin in the hmwk section thot id take a shot here..

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!

and i did get a sol'n from sum1 but i had a question abt it...some1 b kind enuf 2 help!
 

Answers and Replies

  • #2
Astrophysics
61
0
f^-1 = 1/f

1/((2e^x -8)/(10e^x + 9)) = (10e^x + 9)/(2e^x -8)

then you can work to write this function simpler.
 
  • #3
KLscilevothma
322
0
f-1 is the inverse of f, where f is a function.

f-1 does not equal 1/f
 
  • #4
Astrophysics
61
0
if x^-1 = 1/x
it would mean the same for a function, so

f^-1 would be the same as 1/f
 
  • #5
Originally posted by Astrophysics
if x^-1 = 1/x
it would mean the same for a function, so

f^-1 would be the same as 1/f
Sorry, you're wrong Astrophysics. If f is a function then f^-1 is the inverse of the function so that f^-1(f(x)) = x.
 
Last edited by a moderator:
  • #6


Originally posted by sonya
ok...since no1s helpin in the hmwk section thot id take a shot here..

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!

and i did get a sol'n from sum1 but i had a question abt it...some1 b kind enuf 2 help!

You just need some algebraic manipulation first

f = (2e^x -8)/(10e^x + 9)
so, 10e^x * f + 9f = 2e^x -8
so, 10e^x * f - 2e^x = -8 - 9f
so, e^x ( 10f - 2 ) = -( 8 + 9f )
so, e^x = -( 8 + 9f ) / ( 10f - 2 )
so, x = ln[ ( 8 + 9f ) / ( 2 - 10f ) ]
so, x = ln( 8 + 9f ) - ln( 2 - 10f )

therefore f^-1(x) = ln( 8 + 9x ) - ln( 2 - 10x )
 
  • #7
Astrophysics
61
0
Originally posted by MathNerd
Sorry, you're wrong Astrophysics. If f is a function then f^-1 is the inverse of the function so that f^-1(f(x)) = x.


oh thanks mathnerd, but...how come when I put this in my calculator I get f^-1 = 1/f and f^-1(f(x)) is not x?
 
  • #8
Originally posted by Astrophysics
oh thanks mathnerd, but...how come when I put this in my calculator I get f^-1 = 1/f and f^-1(f(x)) is not x?

Because your calculator thinks you're talking about the multiplicative inverse. It doesn't realize that you really want the inverse of the function. In mathematical notation f^-1(f(x)) = f(f^-1(x)) = x e.g. cos^-1 x does not equal 1 / cos x, it is instead inverse cos which is the inverse function of the cosine function. In my last post where I solved for f^-1(x), you can easily show that f(f^-1(x)) = f^-1(f(x)) = x
 
  • #9
Astrophysics
61
0
I'm very confused here, I was actually thinking the same thing as my calculator I guess, but I have no idea what these inverse means, is it f^-1 or is it something like f' ?
 
  • #10
MathematicalPhysicist
Gold Member
4,699
369
Originally posted by MathNerd
Because your calculator thinks you're talking about the multiplicative inverse. It doesn't realize that you really want the inverse of the function. In mathematical notation f^-1(f(x)) = f(f^-1(x)) = x e.g. cos^-1 x does not equal 1 / cos x, it is instead inverse cos which is the inverse function of the cosine function. In my last post where I solved for f^-1(x), you can easily show that f(f^-1(x)) = f^-1(f(x)) = x
or you could say cos^-1 x=arccos x
 
  • #11
Originally posted by loop quantum gravity
or you could say cos^-1 x=arccos x
Yes, well ArcCos is nothing but the inverse of the cosine function, whereas 1/cos(x) = sec(x), it is easily shown that sec(x) doesn't equal ArcCos(x). By definition the inverse of an arbitary function f(x) is another function g(x) such that g(f(x)) = f(g(x)) = x. In mathematical notation g(x) = f^-1(x)
 
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  • #12
phoenixthoth
1,605
2
inverses and identities.

unification.

multiplication.
1 is the "multiplicative identity." let x be a nonzero real number.

x * x^-1 = x^-1 * x = 1. in effect, the thing and its inverse cancel, leaving the identity.

functions.
let * stand for the composition of functions. so rather than write
f(g(x)), write f * g (x).

f * f^-1 = f^-1 * f = I. by, "I", i mean the "identity function,"
I(x) = x.

except for zero, all numbers have a mulitplicative inverse. not so for functions. for example, the function f(x) = x^2 has no inverse defined on the set of real numbers. however, if restriced to nonnegative numbers, f does have an inverse, namely the square root of x. that is precisely what will "cancel" or "oppose" the operation of squaring.

cheers,
phoenix
 

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