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Math Help - composite functions

  1. #1
    Junior Member
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    composite functions

    i'm confused....

    If f(x)=3x+5 and g(x)=x^2+2x-3, determine x such that f(g(x))=g(f(x)).
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  2. #2
    Super Member Showcase_22's Avatar
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    f(g(x))=3 \cdot g(x)+5=3x^2+6x-9+5=3x^2+6x-4

    g(f(x))=(3x+5)^2+2(3x+5)-3=9x^2+30x+25+6x+10-3=9x^2+36x+32

    So we require the solutions to 3x^2+6x-4=9x^2+36x+32

    6x^2+30x+36=0

    \Rightarrow x^2+5x+6=(x+3)(x+2)=0

    So the values of x we require are x=-3 and x=-2.
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  3. #3
    Senior Member I-Think's Avatar
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    f(x)=3x+5 and g(x)=x^2+2x-3

    f(g(x))=3(x^2+2x-3)+5
    g(f(x))=(3x+5)^2+2(3x+5)-3

    Equate these two expressions and solve to answer your question

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