Let a be a real number, f (x) = x ^ 2 + x-a + 1, X ∈ R (1) discuss the parity of F (x); (2) if x ≥ a, find the minimum value of F (x) Why does a compare with 1 / 2 and how to find the monotone interval

Let a be a real number, f (x) = x ^ 2 + x-a + 1, X ∈ R (1) discuss the parity of F (x); (2) if x ≥ a, find the minimum value of F (x) Why does a compare with 1 / 2 and how to find the monotone interval

Let a be a real number, f (x) = x & # 178; + x-a + 1, X ∈ R & nbsp; (1) discuss the parity of F (x); (2) if x ≥ a, find the minimum value of F (x); (1) when a = 0, f (x) = x & # 178; + # x + 1 is even function; when a ≠ 0, f (x) = x & # 178; + # x-a + 1 is non odd and non even function

If x belongs to R, what is the maximum value of the function f (x) = min {2-x & # 178;, X}?

That is, the smaller of 2-x ^ 2 and X
It can be seen from the drawing that the maximum value is one of the intersection points of two function images
Let 2-x ^ 2 = X
x^2+x-2=0
x1=1,x2=-2
∵1>-2
The maximum value is 1

For three numbers a, B and C, min {a, B, C} is used to represent the smallest of the three numbers, for example, min {- 1, 2, 3} = - 1, min {− 1 & nbsp;, 2 & nbsp;, & nbsp; a} = a & nbsp; & nbsp; & nbsp; (a ≤ − 1) & nbsp; & nbsp; − 1 & nbsp; & nbsp; (a ＞ − 1)______ ．

When x ﹥ 2, 2x-1 ﹥ x + 1 ﹥ 2-x, ﹥ min {x + 1, 2-x, 2x-1} = 2-x ﹤ 0, when 1 ﹤ x ﹤ 2, 2x-1 ﹥ 2-x, ﹥ min {x + 1, 2-x, 2x-1} = 2-x ﹤ 1, when 1 = x, 2x-1 ﹥ min {x + 1, 2-x, 2x-1} = 1, when 1 ﹥ x, 2-x ﹥ x + 1 ﹥ min {x + 1}