It is known that the quadratic function f (x) = AX2 + BX + C satisfies f (- 1 / 4 + x) = f (- 1 / 4-x), and the two parts of the equation f (x) = 2x are - 1 and 3 / 2 1 find monotone decreasing interval of function y = (1 / 3) ^ f (x)

It is known that the quadratic function f (x) = AX2 + BX + C satisfies f (- 1 / 4 + x) = f (- 1 / 4-x), and the two parts of the equation f (x) = 2x are - 1 and 3 / 2 1 find monotone decreasing interval of function y = (1 / 3) ^ f (x)

From F (- 1 / 4 + x) = f (- 1 / 4-x), we know that the axis of symmetry is x = - 1 / 4, so - B / (2a) = - 1 / 4, get: B = A / 2F (x) = 2x, get ax ^ 2 + (b-2) x + C = 0, two for - 1,3 / 2, then (2-B) / a = - 1 + 3 / 2 = 1 / 2, that is, 2-B = A / 2, so simultaneous B = A / 2, get: 2-B = B, get; b = 1, so a = 2C / a = - 1 * 3 / 2 = - 3 / 2, get: C = - 3A / 2 = -

FX is a quadratic function, F0 is equal to 1, FX minus 1) minus FX is equal to 4x, find FX

Because f (0) = 1, for that formula F (x-1) - f (x) = 4x, f (- 1) = f (0). Therefore, x = - 1 / 2 is the axis of symmetry. According to f (0) = 1, then f (x) = (x + 1 / 2) ^ 2 + 3 / 4

F (x) is a quadratic function and f (0) = 3, f (x + 2) - f (x) = 4x + 2. Try to find out the analytic expression of F (x). Who can explain it more clearly

Let f (x) = ax ^ 2 + BX + 3 and f (x + 2) - f (x) = 4x + 2, we can see that f (2) - f (0) = 4 × 0 + 2 = 2, that is, f (2) - 3 = 2, then f (2) = 5. Similarly, f (0) - f (- 2) = 4 × (- 2) + 2 = - 6, that is, 3-F (- 2) = - 6, so f (- 2) = 9 has: = 4A + 2B + 3 = 5 （1） 4a-2b+3=9…… (2) Solution (1

Let f (x) = x + 3 / x-a under the root sign. If f (x) is an increasing function on (1, infinity), what is the value range of a

Original = (x-a + A + 3) / radical x-3
=Radical x-a + (a + 3) / radical x-a
Is commonly known as the Nike function
When root x-a = (a + 3) / root x-a
When is the minimum value of the function, corresponding to x = 3 + 2A
So 3 + 2A > 1 is enough
a＞-1
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