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!

Composite of piecewise functions

  1. Nov 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Find f°g for each pair of functions f and g.


    2. Relevant equations

    f(x) = {x+1, if x≤0 or 2x, if x>0

    g(x) = {2x, if x≤-1 or -x, if x>-1

    3. The attempt at a solution

    I am able to determine the following:

    (f°g)(x) = {2x+1, -2x, -x+1

    However, these functions carry intervals, and I don't know how to obtain those intervals

    For example, my book gives the following solution,

    (f°g)(x) = {2x+1, if x≤-1 or -2x, if -1<x<0 or -x+1, if x≥0

    I can obtain the equations, but I don't know how to determine the actual intervals for the individual equations.

    Could someone please explain it to me?
     
  2. jcsd
  3. Nov 17, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    It may help to graph the functions.

    You're looking for (f○g)(x) = f(g(x)) .

    You will have to look at g(x), to see what portion of the domain of g(x) has a range that's in the interval, (-∞, 0] and what portion of the domain of g(x) has a range that's in the interval, (0, +∞) .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Composite of piecewise functions
  1. Piecewise functions (Replies: 5)

  2. Piecewise functions (Replies: 9)

  3. Piecewise functions (Replies: 7)

  4. Piecewise Function (Replies: 1)

Loading...