1.y=(x+2)/(x+1)(x∈[-5,2))2.y=(x+1)/(x^2-2x-8)

Question

1.y=(x+2)/(x+1) (x∈[-5,2))
2.y=(x+1)/(x^2-2x-8)

Answer 1

1、x=-1,分母为0,是间断点,且在[-5,2]区间内,若x从左边趋近-1时,即x+1→0-,则y→-∞,
若x从右边趋近-1 时,即x+1→0+时,y→+∞,
y=1+1/(x+1),
x=-2,y等于0,
求反函数,x=(2-y)/(y-1),y≠1,
∴y∈(-∞,1)∪(1,+∞).
2、y=(x+1)/[(x-4)(x+2)],
当 x→4或x→-2时,y→∞,x=-1时,y=0,
∴y取所有实数,
∴y∈R,即y∈（-∞,+∞）.