f(x)=1/(x²-2x+3)=1/(x²-2x+1+2)=1/[(x-1)²+2]
平方项恒非负,(x-1)²≥0
(x-1)²+2≥2≠0,无论x取何实数,函数表达式始终有意义,函数定义域为R.
1/[(x-1)²+2]≤1/(0+2)=1/2
1>0 (x-1)²+2>0 f(x)>0
0