For each pair a, b with a ∈ R − {0} and b ∈ R, define...

For each pair a, b with a ∈ R − {0} and b ∈ R, define a function fa,b : R → R by fa,b(x) = ax + b for each x ∈ R.

(a) Prove that for each a ∈ R − {0} and each b ∈ R, the function fa,b is a bijection.

(b) Let F = {fa,b | a ∈ R − {0}, b ∈ R}. Prove that the set F with the operation of composition of functions is a non-abelian group. You may assume that function composition is associative.

Expert Solution

Colby Messinger answered 2 years ago

. Recall from the previous page that for each pair a, b with a ∈ R...

. Recall from the previous page that for each pair a, b with a ∈ R − {0} and b ∈ R, we have a bijection fa,b : R → R where fa,b(x) = ax + b for each x ∈ R. (b) Let F = {fa,b | a ∈ R − {0}, b ∈ R}. Prove that the set F with the operation of composition of functions is a non-abelian group. You may assume that function composition is associative

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For each pair a, b with a ∈ R − {0} and b ∈ R, define...

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