求y=x²-x+1/x²-2x+2的值域

求y=x²-x+1/x²-2x+2的值域
求y=x²-x+1/x²-2x+2的值域

求y=x²-x+1/x²-2x+2的值域
Y= (X^2 -2X+2 +X -1)/(x²-2x+2)
=1 + (X-1)/(x²-2x+2)
=1 + (X-1)/[(X-1)^2 +1 ]
当X=1时 Y=1
当 X=1 时
Y=1+1/[(X-1) +1/(X-1)]
X-1 +1/(X-1) 的值域是 (负无穷 ,-2]U[2,正无穷]
所以 Y的价域是[1/2,3/2]