1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Final exam - help- Inverse function Theorem

  1. Apr 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Let f(x) = sinh(x) and let g be the inverse function of f. Using inverse function theorem, obtain g'(y) explicitly, a formula in y.

    Okay the Inverse function Theorem says (f^-1)'(y) = 1/(f'(x))
    If f is continuous on [a, b} and differentiable with f'(x)[itex]\neq[/itex]0 for all x[itex]\in[/itex][a, b]. Then f is 1-1 and f^-1 is continuous and differentiable on f(a,b).

    2. Relevant equations

    3. The attempt at a solution
    The derivative of f(x) sinh(x) is cosh = (e^x + e^-x)/2

    How do I get g'(y) as a formula in y? Right now, I have 2/(e^x + e^-x)
    Last edited by a moderator: Apr 30, 2012
  2. jcsd
  3. Apr 30, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You have ##\frac 1 {f'(x)} = \frac 1 {\cosh x}##, and you have ##y=\sinh x##. It is almost always a mistake to put in exponentials. Use the basic sinh and cosh identity to express ##\cosh x## in terms of ##y##, given what you have.
  4. Apr 30, 2012 #3
    Thanks so much, you save me from messing with exponents! Since I know cosh (x) = √(1 + sinh(x)^2 = √1 + y^2 !
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook