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Homework Help: G(f(x)) Im so lost.

  1. Aug 18, 2011 #1
    1. The problem statement, all variables and given/known data

    g(f(x))
    g(x) = 3/x+1
    f(x)= 3x+2



    2. Relevant equations

    ?

    3. The attempt at a solution

    Ive had none I dont even know how to attempt this problem.
     
  2. jcsd
  3. Aug 18, 2011 #2

    dynamicsolo

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    When you see a composite function, say, g( f(x) ) , that is saying that we will substitute the function f(x) everywhere that 'x' appears in the expression for g(x) . In your problem, this will mean that if g(x) = 3/x+1 ,

    by the way, is this [tex]\frac{3}{x+1} or \frac{3}{x} + 1 [/tex] (I will assume the first -- if you don't use TeX, be sure to use parentheses)

    you would start with

    g( f(x) ) = 3 / [ f(x) + 1 ] = 3 / [ ( 3x + 2 ) + 1 ] ,

    and make any necessary algebraic simplifications from there.
     
  4. Aug 18, 2011 #3
    every were you see x in g(x) plug in f(x)
     
  5. Aug 18, 2011 #4

    I like Serena

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    Welcome to PF, Deagonx! :smile:

    Try it like this:
    g(f(x))
    g(u) = 3/u+1
    u = f(x) = 3x+2
     
  6. Aug 18, 2011 #5

    Ray Vickson

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    Maybe you know whether g(x) = 3/(x+1) or g(x) = (3/x) + 1, but nobody else does. Which one do you mean? (If I read it according to *standard rules*, it means the second form.)

    RGV
     
  7. Aug 19, 2011 #6
    They way that I did it was as followed:

    If f(x) = 3x + 2. and the equation is g(f(x)) then isn't it really just g(3x+2)

    In which case, I came to 3/(3x+2) + 1 which I then simplified to x + 2.5 Which I think is wrong.
     
  8. Aug 19, 2011 #7

    dynamicsolo

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    This part is correct.

    So [tex] f( g(x) ) = \frac{3}{(3x+2) + 1 } = \frac{3}{3x + 3} .[/tex] What would that simplify to?
     
  9. Aug 19, 2011 #8

    x + 1?
     
  10. Aug 19, 2011 #9

    dynamicsolo

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    This is a ratio: what can be done in the numerator and denominator? (Remember, the 3x + 3 is in the denominator.)
     
  11. Aug 19, 2011 #10

    Mentallic

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    And remember, if the original expression is equal to your new expression, whatever value of x you choose (granted you don't divide by zero), you should be able to plug it into both expressions and the same answer will come out!
     
  12. Aug 19, 2011 #11

    uart

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    The first part was correct, but the simplification was wrong.

    To simplify that expression first put everything on a common denominator.

    [tex]\frac{3}{3x+2} + 1 = \frac{3}{3x+2} + \frac{3x+2}{3x+2} [/tex]

    Then simplify it from there.
     
  13. Aug 19, 2011 #12

    dynamicsolo

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    Evidently, everyone still hasn't settled on what g(x) is. So at least we'll have both possible versions...

    By the way, in this version,
    [tex] f( g(x) ) = \frac{3}{(3x+2) + 1 } = \frac{3}{3x + 3} ,[/tex]

    you are dividing 3 by ( 3x + 3 ) , not ( 3x + 3 ) by 3 : that's why this version isn't x + 1 .
     
  14. Aug 19, 2011 #13

    uart

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    Yes it's difficult when the OP wont clarify that, even after being prompted a few times. :frown:

    But without any other clarification I think we really have to go with what the OP is typing, whether or not that is really what he/she is actually trying to ask. :smile:
     
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