Given that f (x) is an odd function, and when x > 0, f (x) = x ^ 3 + 2x ^ 2-1, find the expression of F (x) on X ∈ R

Given that f (x) is an odd function, and when x > 0, f (x) = x ^ 3 + 2x ^ 2-1, find the expression of F (x) on X ∈ R

1. When x > 0, f (x) = x & # 179; + 2x & # 178; - 1;
2. When x = 0, f (x) = 0;
3. If x0, because f (x) is an odd function, then f (x) = - f (- x); if - x > 0, then f (- x) = (- x) & # 179; + 2 (- x) & # 178; - 1 = - X & # 179; + 2x & # 178; - 1, then

Given the function FX = LG ((a ^ 2-1) + (a + 1) x + 1), if its range is r, find the value range of A

(1) The definition field of F (x) is R  (A2-1) x2 + (a + 1) x + 1 > 0
When A2-1 = 0, a = - 1, a = 1 does not hold
When A2-1 ≠ 0,
a2−1＞0
△＝(a+1)2−4(a2−1)＜0
The solution is a > 3 / 5
Or a ＜ - 1
In conclusion, a > 3 / 5
Or a ≤ - 1
(2) When A2-1 = 0, a = 1, a = - 1 does not hold
When A2-1 ≠ 0,
a2−1＞0
△＝(a+1)2−4(a2−1)≥0
The solution is 1 ＜ a ≤ 3 / 5
In conclusion, 1 ≤ a ≤ 3 / 5
PS: you're missing an X ^ 2, otherwise you can't work it out