If the image of function f (x) = x ^ 2 + MX + 1 is symmetric with respect to x = 1, what is the value set of real number m?

If the image of function f (x) = x ^ 2 + MX + 1 is symmetric with respect to x = 1, what is the value set of real number m?


I'm from high school. I should have learned the axis of symmetry of quadratic function
X = - B / 2A (B is the coefficient of the first term, a is the coefficient of the second term)
This problem a = 1, B = m is symmetric about x = 1
That is, 1 = - M / (2 * 1)
The solution is m = - 2
Is that clear?



Let f (x) defined on the set of real numbers have f (x) + F (2-x) = 1 for any x, then the image of this function must be about what symmetry?


Let point (a, b) be any point on the image of function f (x), then B = f (a) is known: for any x, f (x) + F (2-x) = 1, then f (2-A) = 1-f (a) and B = f (a), so f (2-A) = 1-b. this shows that point (2-A, 1-B) is also on the function image, and point (a, b) is the same as point (a, b)



Given a = 5 − 12, f (x) = ax, if real numbers m and N satisfy f (m) > F (n), then the size relation of M and N is ()
A. M = NB. M < NC. M > nd


∵ a = 5 − 12, ∵ 0 < a < 1. The function f (x) = ax decreases monotonically on R, and ∵ real numbers m and N satisfy f (m) > f (n), ∵ m < n



Find a positive zero of function f (x) = X3 + x2-2x-2 (accuracy 0.1)


Because f (1) = - 2 < 0, f (2) = 6 > 0, the interval (1,2) can be taken as the initial interval of calculation, and the dichotomy method is used to calculate step by step. The list is as follows: the function value of endpoint or midpoint coordinates takes the interval A0 = 1, B0 = 2, f (1) = - 2 < 0, f (2) = 6 > 0 (1,2)