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Let f and g be real - valued functions s...

Let f and g be real - valued functions such that `f(x+y)+f(x-y)=2f(x)*g(y), forall " x , y " in R.` Prove that , if f(x) is not identically zero and `abs(f(x)) le 1, forall x in R,` then `abs(g(y)) le 1, forall y in R.`

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