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Thread: combined functions

  1. March 8th 2009, 07:46 AM #1
    jlefholtz
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    combined functions

    I am having a terrible time with this combined function.

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

    f(g(x))=?

    I don't remember much from Algebra 1 and 2 in highschool, it was ten years ago and I'm sure I covered this there. Now I'm wishing I'd taken college algebra before enrolling in precalc.

    Help?

    Thank you,
    Jonah Lefholtz
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  2. March 8th 2009, 07:51 AM #2
    mathaddict
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    Quote Originally Posted by jlefholtz View Post
    I am having a terrible time with this combined function.

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

    f(g(x))=?

    I don't remember much from Algebra 1 and 2 in highschool, it was ten years ago and I'm sure I covered this there. Now I'm wishing I'd taken college algebra before enrolling in precalc.

    Help?
    fg(x)=f[\frac{3x+1}{-x+2}]

    =\frac{2(\frac{3x+1}{-x+2})-1}{\frac{3x+1}{-x+2}+3}
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  3. March 8th 2009, 10:04 AM #3
    stapel
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    Talking

    Quote Originally Posted by jlefholtz View Post
    f(x)= 2x-1/x+3 and g(x)=3x+1/-x+2

    f(g(x))=?

    I don't remember much from Algebra 1 and 2 in highschool...
    To refresh your memory, try these lessons on function composition and simplifying "complex" fractions.
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  4. March 8th 2009, 06:04 PM #4
    jlefholtz
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    Quote Originally Posted by mathaddict View Post
    fg(x)=f[\frac{3x+1}{-x+2}]

    =\frac{2(\frac{3x+1}{-x+2})-1}{\frac{3x+1}{-x+2}+3}
    Okay, that's as far as I got. It doesn't simplify any more? The solution my professor gave us says the answer to the function is "x" however, I couldn't derive it.

    Thank you.
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  5. March 8th 2009, 07:37 PM #5
    mathaddict
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    Quote Originally Posted by jlefholtz View Post
    Okay, that's as far as I got. It doesn't simplify any more? The solution my professor gave us says the answer to the function is "x" however, I couldn't derive it.

    Thank you.
    Oh no , i stopped there to just let you continue .

    Well , continue simplifying :

    \frac{\frac{6x+2+x-2}{-x+2}}{\frac{3x+1-3x+6}{-x+2}}

    =\frac{7x}{7}

    <br /> =x<br />
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  6. March 8th 2009, 08:32 PM #6
    jlefholtz
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    thanks again

    Ok. Thanks again. I keep getting 7x-3/7 so I'm close...I just need to figure out what I'm doing wrong. Thanks!
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