Given that the function f (x) = (A-2) x & # 178; + (A-1) x + 3 is even, then the monotone increasing interval of F (x) is?

Given that the function f (x) = (A-2) x & # 178; + (A-1) x + 3 is even, then the monotone increasing interval of F (x) is?

Because f (x) = (A-2) x ^ 2 + (A-1) x + 3 is an even function,
f(-x)=(a-2)(-x)^2+(a-1)(-x)+3
=(a-2)x^2+(1-a)x+3
=(a-2)x^2+(a-1)x+3
So A-1 = 1-A
That is, a = 1, f (x) = - x ^ 2 + 3
The symmetry axis is y-axis, the opening is downward, and the monotone increasing interval of function f (x) is (- ∞, 0]
If you don't understand, please ask
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