If f (x) is a quadratic function and f (0) = 1, f (2x + 1) - f (x) = 2, find f (x) | Math enthusiast | Mathematical art

If f (x) is a quadratic function and f (0) = 1, f (2x + 1) - f (x) = 2, find f (x)

Let f (x) = ax ^ 2 + BX + C, (a ≠ 0) denote f (0) = 1, so C = 1
F (2x + 1) - f (x) = a (3x ^ 2 + 4x + 1) + B (x + 1) = 3ax ^ 2 + (4a + b) x + (a + b) = 2 is constant, and a ≠ 0 is obviously impossible, so there is no f (x) satisfying the meaning of the problem

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