Given the function f (x) = (radical 3) sin2x + cos2x, if f (x-a) is even, then a value of a is

f(x)=2（sin2xsinπ/3+cosπ/3cos2x)=2cos(2x+π/3)
f(x-a)=2cos[2(x-a)+π/3]=2cos[2(x-a+π/6)]
When f (x-a) is an even function, - A + π / 6 may be 0, that is, - A + π / 6 = 0, the solution is a = π / 6

The function f (x) = AX2 + BX + C is even if______ ．

∵ f (x) = AX2 + BX + C is an even function, ∵ f (- x) = f (x), that is, AX2 BX + C = AX2 + BX + C, then a = a − B = BC = C, that is, a, C ∈ R, and B = 0, so the answer is: A, C ∈ R, and B = 0

A necessary and sufficient condition for a function f (x) = ax & sup2; + BX + C (a ≠ 0) to be even

b=0
Filling F1 = F-1
b=0
want
obviously

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