Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Composition and Identity of functions

  1. Aug 30, 2004 #1
    f(x) = 3x + 2 and g(x) = x + 5

    f[g(x)] but some how this equals 3x + 17? plz show me.
    g[f(x)] I know this would equal 3x + 7


    Thanks <3
     
  2. jcsd
  3. Aug 30, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    a function takes the input, performs some operation and gives an output.

    f takes the input, multiplies by 3 and adds 2, now what's the input?
     
  4. Aug 30, 2004 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    f(x)= 3x+ 2 MEANS "what ever is inside the parentheses, multiply it by 3 and then add 2. So f(g(x))= f(x+5) means- multiply x+5 by 3 and then add 2: f(g(x))= 3(x+5)+ 2= what?

    g(x)= x+ 5 MEANS "whatever is inside the parentheses, add 5 to it". g(f(x))= g(3x+2) MEANS "add 5 to 3x+ 2". What is that?
     
  5. Aug 31, 2004 #4

    Alkatran

    User Avatar
    Science Advisor
    Homework Helper

    f(x) = 3x + 2
    g(x) = x + 5
    f(g(x)) = ?

    First off, let's make things easier for you and say that:
    y = g(x)
    which means:
    f(g(x)) = f(y)

    Now what is y?
    y = g(x) = x + 5
    And what is f(y)?
    f(y) = 3y + 2
    since y = g(x) = x + 5 we can replace y with x + 5
    3y + 2 = 3(x + 5) + 2
    Then take x + 5 out of paratheses:
    3(x + 5) + 2 = 3x + 15 + 2 = 3x + 17
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Composition and Identity of functions
  1. Composite Functions (Replies: 3)

  2. The identity function (Replies: 2)

Loading...