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For each pair a, b with a ? R ? {0} and b ? R,...

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Advance Math

For each pair a, b with a ? R ? {0} and b ? R, define a functionfa,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 functionfa,b is a bijection.

(b) Let F = {fa,b | a ? R ? {0}, b ? R}. Prove that the set Fwith the operation of composition of functions is a non-abeliangroup. You may assume that function composition is associative.

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