Results 1 to 2 of 2

Math Help - Domain range and inverse of natural log function

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Ny
    Posts
    17

    Domain range and inverse of natural log function

    Let f be the function given by f(x)=ln(x/x-1)
    A) what is the domain and range of f
    B) what is the inverse of f
    C) what is the range of the inverse,justify

    So when I started this problem I got the domain to be (-infinity,0),(1,infinity) because the restriction in the domain of 1 and 0. For the range I think it is a limit issue but I don't know how to get that and for the inverse I can't figure out how to get rid of the y-1 in the denominator after I raise both sides under base e to get rid of the ln. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,115
    Thanks
    992

    Re: Domain range and inverse of natural log function

    (a) agree with your domain.

    for the range, consider the first domain interval (-\infty,0) ... as x \to -\infty, \frac{x}{x-1} \to 1 and as x \to 0^- , \frac{x}{x-1} \to 0 ... the range of the log function over this interval is (-\infty, 0).

    now consider the other interval of the domain (1, \infty) ... as x \to 1^+, \frac{x}{x-1} \to \infty and as x \to \infty , \frac{x}{x-1} \to 1 ... the range of the log function over this interval is (0, \infty).

    I'd say the range is all reals except y = 0

    (b) inverse ...

    x = \ln\left(\frac{y}{y-1}\right)

    \frac{y}{y-1} = e^x

    y = ye^x - e^x

    e^x = ye^x - y

    e^x = y(e^x-1)

    y = \frac{e^x}{e^x - 1}

    (c) ... wouldn't the range of the inverse be the domain of the original function?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 20th 2012, 08:08 PM
  2. Domain/Range of Inverse Trig Function
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 10th 2011, 08:12 PM
  3. Replies: 1
    Last Post: April 11th 2010, 02:04 PM
  4. Domain and Range of the Inverse Quadratic Function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 29th 2009, 03:31 PM
  5. inverse function and domain and range
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 14th 2008, 03:45 AM

Search Tags


/mathhelpforum @mathhelpforum