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H ow we can writting g(x)=\alpha y+ \beta z that \alph^s+\beta^s=1 and y,z are terms a,b

Example:If g be a function from [a,b] into real number. we have g(x)=g((1-(x-a/b-a))a +(x-a/b-a)b).

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I don't think anyone has answered your question Razieh because it is incomprehensible.  Try rewriting your question more carefully...