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Math Help - composite functions :o

  1. #1
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    composite functions :o

    1)If f(x)=3x+5 and g(x)=x^2+2x-3, determine x such that f(g(x))=g(f(x)).

    2)If f(x)=2x-7 and g(x)=5-2x,
    a)determine fof^-1 and f^-1of.
    b)show that (fog)^-1=g^-1of^-1

    thank you =)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by johett View Post
    1)If f(x)=3x+5 and g(x)=x^2+2x-3, determine x such that f(g(x))=g(f(x)).
    we want 3(x^2 + 2x - 3) + 5 = (3x + 5)^2 + 2(3x + 5) - 3

    now solve for x

    2)If f(x)=2x-7 and g(x)=5-2x,
    a)determine fof^-1 and f^-1of.
    i suppose they want us to do this the hard way. so first thing's first. find f^{-1}(x) and then we'll take it from there.

    b)show that (fog)^-1=g^-1of^-1

    thank you =)
    find (f \circ g)(x) and then it's inverse

    then find g^{-1}(x) (you already found f^{-1}(x)

    then just show that both expressions are equal. that is, find and simplify (f \circ g)^{-1}(x) and show that you get the same expression as when you find and simplify (f^{-1} \circ g^{-1})(x)
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  3. #3
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    for the first question i got...

    3 x^2+6x-9+5=(3x+5) ^2+2(3x+5)-3
    3 x^2+6x-4=9 x^2+15x+15x+25+6x+7
    3 x^2+6x-4=9 x^2+36x+32
    is this answer close to the final answer?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by johett View Post
    for the first question i got...

    3 x^2+6x-9+5=(3x+5) ^2+2(3x+5)-3
    3 x^2+6x-4=9 x^2+15x+15x+25+6x+7
    3 x^2+6x-4=9 x^2+36x+32
    is this answer close to the final answer?
    why don't you finish?

    by the way, it's ok to type the whole line between the math tags. it looks weird when you just put the x-squared in there

    doesn't 3x^2 + 6x - 9 + 5 = (3x + 5)^2 + 2(3x + 5) - 3 look better?
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