数学题一道：设函数f(x)的定义域为R,若f(π/2)=0,f(π)=-1设函数f(x)的定义域为R,若f(π/2)=0,f(π)=-1,且对任意的X1X2有f(X1)+f(X2)=2f(X1+X2/2)f(X1-X2/2) (1)求f(0) (2)求证f(X)为偶函数,且f(π-x)=-f(x) (3)若-π/2＜X＜π/2,f(x)＞0,求证f(x)在[0,π]上单调递减. 要详解,感激不尽~~O(∩_∩)O~
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数学题一道：设函数f(x)的定义域为R,若f(π/2)=0,f(π)=-1
设函数f(x)的定义域为R,若f(π/2)=0,f(π)=-1,且对任意的X1X2有f(X1)+f(X2)=2f(X1+X2/2)f(X1-X2/2) (1)求f(0) (2)求证f(X)为偶函数,且f(π-x)=-f(x) (3)若-π/2＜X＜π/2,f(x)＞0,求证f(x)在[0,π]上单调递减. 要详解,感激不尽~~O(∩_∩)O~
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