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Math Help - Composite functions

  1. #1
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    Composite functions

    Am I working this problem properly?
    If f(x)=3x+1, and g(x)=(x^2+5x)^{-\frac{1}{2}}, find g(f(x)).

    Working:
    If f(x)=3x+1, and g(x)=(x^2+5x)^{-\frac{1}{2}} then, g(f(x))= ((3x+1)^2+5(3x+1))^{-\frac{1}{2}}.

    Am I correct, and is that the final answer?
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  2. #2
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    Quote Originally Posted by koumori View Post
    Am I correct,
    Yep

    Quote Originally Posted by koumori View Post
    and is that the final answer?
    Expand inside the main bracket and group like terms to simplify
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Yep



    Expand inside the main bracket and group like terms to simplify

    Ok...so the final answer looks like this:
    ((9x^2+1)+(15x+5))^{-\frac{1}{2}}\rightarrow \frac{1}{\sqrt{(9x^2+1)+(15x+5)}}?
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  4. #4
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    Actually, what you should have found was that the expression simplifies to

    ((9x^2 + 6x + 1) + (15x + 5))^{-\frac{1}{2}},

    and that can be further simplified to

    (9x^2 + 21x + 6)^{-\frac{1}{2}}.

    You can also take out a factor of 3:

    (3(3x^2 + 7x + 2))^{-\frac{1}{2}}
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  5. #5
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    Quote Originally Posted by koumori View Post
    Ok...so the final answer looks like this:
    ((9x^2+1)+(15x+5))^{-\frac{1}{2}}\rightarrow \frac{1}{\sqrt{(9x^2+1)+(15x+5)}}?
    No, (3x+1)^2 \neq 9x^2+1
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  6. #6
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    Quote Originally Posted by icemanfan View Post
    Actually, what you should have found was that the expression simplifies to

    ((9x^2 + 6x + 1) + (15x + 5))^{-\frac{1}{2}},

    and that can be further simplified to

    (9x^2 + 21x + 6)^{-\frac{1}{2}}.

    You can also take out a factor of 3:

    (3(3x^2 + 7x + 2))^{-\frac{1}{2}}
    Quote Originally Posted by pickslides View Post
    No, (3x+1)^2 \neq 9x^2+1
    I see! Because I should use F.O.I.L on (3x+1)^2 making it
    ((9x^2 + 6x + 1) + (15x + 5))^{-\frac{1}{2}}. Then I have to do simple addition of like terms to net a result of (9x^2 + 21x + 6)^{-\frac{1}{2}}. Then do as you said and factor everything by 3.
    Finally, expand the exponent so (9x^2 + 21x + 6)^{-\frac{1}{2}} becomes: \frac{1}{\sqrt{(9x^2 + 21x + 6)}}

    Funny how I lost my head at this once the big words came out.......

    Thank you for your help guys!
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