If f(x)+f(y)+f(xy)=2+f(x).f(y). f(x) IS POLYNOMIAL FUNCTION WHERE f(4)=17. FIND f(5)

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That the functional equation f(x) + f(1/x) = f(x).f(1/x) has f(x) = xⁿ+1 is not a standard result!

The equation can be written as f(xy)-1 = ( f(x) -1 ) ( f(y) - 1)

Setting g(x) = f(x) -1, we have g(xy) = g(x) g(y) for which all solutions are given by g(x) = |x|^c for some constant c.

So that f(x) = |x|^c+1

Here from f(4) = 17, we obtain c = 2 and hence f(5) = 26

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