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Composite functions

  1. Jul 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine each of the following composite functions:
    a) gof(x)
    b)foh(x)


    2. Relevant equations
    Where f(x)=e^(3x+2) [e is the exponential function]
    g(x)= ln(4x+1)
    h(x)= 1/(2x-1)


    3. The attempt at a solution
    So I have found an answer, I am just unsure if I am correct though. This is what I did:

    a) gof(x)=g(f(x))
    = ln(4(f(x)+1)
    =ln(4e^(3x+2)+1)
    = ln4e^(3x+2)+ln1
    =(3x+2)*4*lne+ln1
    = 4(3x+2)+ln1
    =12x+8+ln1
    =12x+8

    b)foh(x)=f(h(x))
    =e^(3(h(x))+2)
    =e^(3(1/(2x-1))+2)
    =e^(3/(2x-1))+2)


    Is this the correct working out and answers?
     
    Last edited: Jul 17, 2012
  2. jcsd
  3. Jul 17, 2012 #2

    ehild

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    Gold Member

    Neither the logarithm nor the exponential are additive functions.

    ehild
     
  4. Jul 17, 2012 #3
    what does that mean and how does it affect my final answers?
     
  5. Jul 17, 2012 #4

    ehild

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    Homework Helper
    Gold Member

    ln(A+B)≠lnA+lnB. eA+B≠eA+B.
    Also check your parentheses.


    ehild
     
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