Results 1 to 3 of 3

Math Help - Range of f(x)?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Range of f(x)?

    Given the functions
    f(x) = \exp(\arccos \left(\sin \left(x + \frac{\pi}{3}\right)\right)),
    g(x) = \mbox{arccsc} \left(\frac{4 - 2\cos x}{3}\right)
    and the function h(x) = f(x) defined only for the common domain of f(x)\ \mbox{\&}\ g(x).

    Calculate range of h(x).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    Since sines and cosines take on the same values,

    f(x)=\exp\left(\arccos\left(\sin\left(x+\frac{\pi}  {3}\right)\right)\right)

    is defined everywhere, i.e., its domain is \mathbb{R}. The domain of h is therefore just the domain of g, consisting of precisely the values of x for which

    \frac{4-2\cos x}{3}

    belongs to (-\infty,-1]\cup[1,\infty). When we find these values, we can use them to find the range of h on that domain.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539
    How do we find these values?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Range of b
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 18th 2011, 08:26 AM
  2. range
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 10th 2011, 10:06 AM
  3. range
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: March 27th 2010, 05:46 AM
  4. Replies: 6
    Last Post: September 16th 2009, 06:25 AM
  5. range, inter-quartile range
    Posted in the Statistics Forum
    Replies: 1
    Last Post: June 19th 2006, 05:06 AM

Search Tags


/mathhelpforum @mathhelpforum