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!

Inverse Equation and if Values exist!

  1. Feb 11, 2009 #1
    Please help me with these following problems:

    1.)Indicate whether each of the following functions is invertible in the given interval. Explain

    a.) sech x on [0,infinity)

    b.) cos (ln x) on (O, e^pie]

    c.) e^(x^2) on (-1,2]


    My work process for a: let y= sech x

    how do i find x in terms of y for this eq. how do i isolate the x variable from sech x.

    once I find that i can see if the positive values of x for the inverse function exist from 0 to infinity.

    however, i need help finding the inverse function


    My work process for b.) let y= cos (ln x)

    I took the expotential of both sides to get

    e^y= e^(cos*(lnx))

    how do i isoloate e*(lnx) to equal x , since the lnx is a part of the cosine angle expression.. i need help here...

    once i find the inverse equation, i can see if y values exists for the x values from 0 to e^pie... i need help finding the inverse equation first



    My work process for c.) let = y= e^(x^2)

    therefore taking the natural logarithm of both sides i get


    ln y= ln (e^(x^2)
    ln y= x^2

    therefore x= sqrt (ln y)

    therefore f^-1 (x)---> inverse function is f(x)= sqrt (ln x)

    when subbing (-1,2] for x to determine if y values exist,

    i find the inverse function doesn't exist under those limits since ln 0 is undefined

    is this the correct approach to this problem.


    Please help me with these problems!
     
  2. jcsd
  3. Feb 11, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    A function is invertible in an interval if it is "one-to-one" there: that is, that two different values of x in the interval that give the same value of y. It should be fairly obvious, for example, that (-.5)2= .52 so [itex]e^{(-.5)^2}= e^(0.5)^2[/itex].

    You say at one point
    which is not true: if ln y= x^2 then either x= sqrt(ln y) or x= -sqrt(ln y).

    Your point about ln(0) not existing is a good one.

    For the others try looking at graphs of the functions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inverse Equation and if Values exist!
  1. Inverse trig value (Replies: 1)

Loading...