Question: Let g : R R be defined as g(x) = 2x instead? Find functions g1 : R R and g2 : R R such that

Let g : R R be defined as g(x) = 2x instead? Find functions g1 : R R and g2 : R R such that the following three properties hold:

g1 is even,

g2 is odd,

g1 + g2 = g.

Justify your responses, but no formal proof is necessary. Simplify g1 and g2 where possible.

Hint: g(1) = 2 and g(1) = 1 /2 . From this and the definition of even/odd functions, first determine g1(1), g2(1), g1(1), and g2(1).

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