# Math Help - Translation function

1. ## 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

2. Originally Posted by jzellt
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?

3. 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??

4. Originally Posted by jzellt
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