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对称性是函数的一个重要性质,利用对称性可以解决许多有关函数的问题。下面给出一常用对称定理:若函数y=f(x)关于x=a对称f(a+x)=f(a-x)f(x)=f(2a-x),并举例说明其应用。一、比较大小例1.如果函数f(x)=x2+bx+c对任意实数x都有f(2+x)=f(2-x),则()A.f(2)f(1)f(4)B.f(1)f(2)f(4
Symmetry is an important property of a function. Using symmetry can solve many problems with functions. A common symmetry theorem is given below: If the function y=f(x) is symmetrical about x=a f(a+x)=f(a-x)f(x)=f(2a-x), and its application is illustrated. First, compare the size of the example 1. If the function f (x) = x2 + bx + c for any real number x has f (2 + x) = f (2-x), then () Af (2) f (1) f(4)Bf(1)f(2)f(4