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已知偶函数f(x),对任意X1,X2,恒有f(X1+X2)=f(X1)+f(X2)-2X1X2+1 问求f(0),f(1),f(2)的值 求f(x) 判断
F(x)=[f(x)]平方-2f(x)有无最值,如有,求出其最值
人气:419 ℃ 时间:2020-09-10 01:43:15
解答
先令x1 = x2 = 0可得f(0) = -1;
f(x - x) = f(x) + f(-x) + 2x^2 + 1 ==> f(0) = f(x) + f(x) + 2x^2 + 1
f(x + x) = f(x) + f(x) -2x^2 + 1
两式相减得:
f(0) - f(2x) = 4x^2 = (2x)^2
即:
f(2x) = f(0) - (2x)^2
所以f(x) = -1 - x^2
f(x)出来了那其他的就好办了,求导可知F(x)有最小值3
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