Given f : → and g : → , we define the sum f + g by (f + g)(x) = f(x) + g(x) and the product fg by (fg)(x) = f(x).g(x) for all x ∈ Find counterexamples for the following.
(a) If f and g are bijective, then the sum f + g is bijective.
(b) If f and g are bijective, then the product fg is bijective.
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