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Math Help - Translation function

  1. #1
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    Translation function

    Let a e Z. Then the translation function by a is defined to be the function A sub a : Z ---> Z defined by the rule x l--> x + a.

    Prove: If a,b e Z, then A sub a o A sub b = A sub (a+b)

    o = composed with
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jzellt View Post
    Let a e Z. Then the translation function by a is defined to be the function A sub a : Z ---> Z defined by the rule x l--> x + a.

    Prove: If a,b e Z, then A sub a o A sub b = A sub (a+b)

    o = composed with
    Let me start you off.

    note that (A_a \circ A_b) (x) = A_a (A_b(x)) = A_a (x + b)  = \dots

    can you finish?
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  3. #3
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    Let me start you off.

    note that

    can you finish?

    So, Aa(x + b) = (x + b) + a = x + (b + a) = A sub (a+b) (x) .... Is this correct??
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jzellt View Post
    Let me start you off.

    note that

    can you finish?

    So, Aa(x + b) = (x + b) + a = x + (b + a) = x + (a + b) = A sub (a+b) (x) .... Is this correct??
    yup, that's it
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