LetH = {f : R → R | f(x) = ax + b; a, b ∈ R; a 0}.H1 = {f : R → R | f(x) = ax; a ∈ R; a 0}.H2 = {f : R → R | f(x) = x + b; b ∈ R}.(a) Prove that H1 and H2 are subgroups of H.(b) Determine whether each is a normal subgroup of H.

Question

LetH = {f : R → R | f(x) = ax + b; a, b ∈ R; a > 0}.H1 = {f : R → R | f(x) = ax; a ∈ R; a > 0}.H2 = {f : R → R | f(x) = x + b; b ∈ R}.(a) Prove that H1 and H2 are subgroups of H.(b) Determine whether each is a normal subgroup of H.

Let
H = {f : R → R | f(x) = ax + b; a, b ∈ R; a > 0}.
H1 = {f : R → R | f(x) = ax; a ∈ R; a > 0}.
H2 = {f : R → R | f(x) = x + b; b ∈ R}.
(a) Prove that H1 and H2 are subgroups of H.
(b) Determine whether each is a normal subgroup of H.

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