If the function f (x) = 2A & # 178; + (A-1) x + 3 is even, then a=

If the function f (x) = 2A & # 178; + (A-1) x + 3 is even, then a=

Even function, then f (x) = f (- x) for any X. if (A-1) x = (1-A) x is brought in, a = 1 is obtained

If the function f (x) = (K-2) x ^ + (k-1) x + 3 is even, then the increasing interval of F (x) is-------

From the solution of F (x) = f (- x), k-1 = 1-k
k = 1
So f (x) = - x ^ + 3
So the increasing interval is (- infinity, 0)

It is known that f (x) = x & # 178; + (A-1) x is an even function. Then the monotone increasing interval of the function g (x) = ax & # 178; - 2x-t is

Solution
f（-x）=x^2-（a-1）x=x^2+（a-1）x=f（x）
So - A + 1 = A-1, the solution is a = 1
So g (x) = x ^ 2-2x-t
=x^2-2x+1-1-t
=（x-1）^2-1-t
The opening is upward, and the axis of symmetry x = 1
So g (x) is an increasing function at (1, + infinity)