If the domain of function f (x) = LG [(a ^ 2-1) x ^ 2 + (A-1) x + 1] is r, the value range of a is obtained

If the domain of function f (x) = LG [(a ^ 2-1) x ^ 2 + (A-1) x + 1] is r, the value range of a is obtained

The function f (x) = LG [(a ^ 2-1) x ^ 2 + (A-1) x + 1] requires (a ^ 2-1) x ^ 2 + (A-1) x + 1 > 0,
The domain is r,
Then, (1) when a ^ 2-1 = 0,
That is, when a = 1, X belongs to R,
When a = - 1, it does not hold;
(2) When a ^ 2-1 > 0, that is a > 1 or A0,
We can get, A1, and synthesize a

If the definition field of function f (x) = √ (2x ^ 2-2ax-a-1) is r, then the value range of a is?

Let f (x) = 2x ^ 2-2ax-a-1, the opening of the image be upward
To make the domain R, make 2x ^ 2-2ax-a-1 > = 0 hold
Then △ = (- 2A) ^ 2-8 (- A-1)

It is known that y = f (x) is a decreasing function over the domain (- 1), and f (1-A)

Only three conditions need to be met
-1

It is known that y = f (x) is a decreasing function over the domain (- 1,1), and f (- a)

Because the domain is (- 1,1), so - 1