Question

这题的详细过程？谢谢！

Answer 1

(1)
f(x) = (x + 1)(x + 3) = 0
x = -1或x = -3
f(a + 1) = 0, a + 1 = -1或a + 1 = -3
a = -2或a = -4

(2)
g(x) = x² + 4x + 3 + cx = x² + (c+4)x + 3
为偶函数, 则c + 4 = 0, c = -4

(3)
令b > a ≥ -2:
f(b) - f(a) = b² + 4b + 3 - (a² + 4a + 3)
= b² - a² + 4(b - a)
= (b + a)(b - a) + 4(b - a)
= (b - a)(a + b + 4)
b > a ≥ -2, b - a > 0; a + b >-4, a + b +4 > 0
f(b) - f(a) > 0
在x≥ -2时为增函数

或
f(x) = (x + 2)² - 1
此为开口向上, 对称轴为x = -2的抛物线, 在x≥ -2时为增函数