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Solving problems in function notation

  1. Oct 16, 2016 #1
    1. The problem statement, all variables and given/known data
    Given that:
    g (1)=3
    g (2x+1)=4g (x)+x+1

    Find g (3)

    2. Relevant equations
    The awnser is 14. (Taken out of a PSAT workbook)

    3. The attempt at a solution
    I assume that g(2x+1) refers to a series of transformations (horizontal dilation, up 1) of g(x)
    Once g(x) is found, g(3) can easily be solved. The problem is, that I have no idea how to find it.
     
  2. jcsd
  3. Oct 16, 2016 #2

    pasmith

    User Avatar
    Homework Helper

    The second equation tells you how to find [itex]g(2x + 1)[/itex] if you already know [itex]g(x)[/itex].

    For which value of [itex]x[/itex] do you already know [itex]g(x)[/itex]?
     
  4. Oct 16, 2016 #3

    fresh_42

    Staff: Mentor

    To me it appears you think a little bit too complicated.
    Can you write ##3## as ##2x+1## and what does it tell you about ##x##?
     
  5. Oct 16, 2016 #4
    Ah! Your suggestions make sense!

    When substituting x for one,

    g(2(1)+1)=4g(1)+1+1
    g(3)=4(3)+2
    g(3)=12+2
    g(3)=14
     
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