Question

已知二次函数y=f(x)开口向上,且对一切实数x,都有f(x+3)=f(5-x),则f(3.1415926)与f(9/2

Answer 1

f(x + 3) = f(5 -x), x = 0时, f(3) = f(5), 这说明二次函数y=f(x)顶点的横坐标为 x = (3 + 5)/2 = 4

f(x)开口向上, 3.1415926与9/2两点中与4较远的点对应的y值较大.

|3.1415926 - 4| = 0.8584074

|9/2 - 4| = |4.5 - 4| = 0.5 < 0.8584074,

f(3.1415926)> f(9/2)