已知函數(shù)f(x)=(x-1)/(x^2+1),求證：-（根號(hào)2+1）/2〈=f(x)<=(根號(hào)2-1)/2

熱心網(wǎng)友

由y=(x-1)/(x^2+1)，得yx^2-x+y+1=0方程關(guān)于x有解，所以△=1-4y(y+1)≥0y^2+y≤1/4[y+(1/2)]^2≤1/2|y+(1/2)|≤√2/2-√2/2≤y+(1/2)|≤√2/2-(√2+1)/2≤y≤(√2-1)/2既：-(√2+1)/2≤f(x)≤(√2-1)/2

熱心網(wǎng)友

對(duì)

熱心網(wǎng)友

已知函數(shù)f(x)=(x-1)/(x^2+1),求證：-（根號(hào)2+1）/2〈=f(x)<=(根號(hào)2-1)/2 解：令f(x)=(x-1)/(x^2+1)=y則yx^2-x+y+1=０x必定有實(shí)跟，故△＞＝０得：-（根號(hào)2+1）/2〈=f(x)<=(根號(hào)2-1)/2