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Math Help - Help with composites please!

  1. #1
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    Help with composites please!

    Here's the question:

    Find the composites for the relations defined.

    R1={(x,y) member of real numbers x real numbers: y=x}
    R2={(x,y) member of real numbers x real numbers: y=-5x+2}

    a) R1compositeR1
    b)R2compositeR2


    a) I was thinking that R1compositeR1={(x,y) member of real numbers x real numbers: x=y}=R1
    b) I'm not to sure how to do and thats the one I need help on.


    Can you please help me?

    Thank you!!
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  2. #2
    Behold, the power of SARDINES!
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    let
    f(x)=x and g(x)=-5x+2

    Then

    (f \circ g)(x)=g(x)=-5x+2 and

    (g \circ f)(x)=-5f(x)+2=-5x+2

    Since both f and g are defined on all of R and both map onto R

    The domain and Range are all real numbers.

    I hope this helps
    good luck.
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    let
    f(x)=x and g(x)=-5x+2

    Then

    (f \circ g)(x)=g(x)=-5x+2 and

    (g \circ f)(x)=-5f(x)+2=-5x+2

    Since both f and g are defined on all of R and both map onto R

    The domain and Range are all real numbers.

    I hope this helps
    good luck.
    I still don't understand. Does this mean that R2compositeR2={(x,y) member of real numbers x real numbers: y=-5x+2}=R2?
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  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by calcprincess88 View Post
    I still don't understand. Does this mean that R2compositeR2={(x,y) member of real numbers x real numbers: y=-5x+2}=R2?
    R1 and R2 are just fuctions.

    R1= f(x)=x

    R2= g(x)=-5x+2

    I just called R1 f and R2 g

    R2 \circ R2 = g(x) \circ g(x)=g(g(x))=-5g(x)+2=-5(-5x+2)+2=25x-8

    and

    R1 \circ R1 = f(x) \circ f(x)=f(f(x))=f(x)=x
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  5. #5
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    ohhhh I get it. I'm sorry. I didn't understand at first what you were saying but now I do! Thank you soooo much for your patience and help!! I really appreciate it!!!
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