Question

f（x）=|x^2-1|的单调递增区间和单调递减区间

Answer 1

先解不等式x^2-1≥0,得x≥1或x≤-1

所以分区间讨论:

1）x≥1时,f(x)=x^2-1,单调增区间为[1,+∞）;

2) x≤-1时,f(x)=x^2-1,单调减区间为[1,+∞）;

3）-1≤x≤1时,f(x)=1-x^2,单调增区间为[-1,0],单调减区间为[0,1]

所以f(x)=|x^2-1|的单调递增区间为[-1,0]∪[1,+∞）,单调减区间为[-∞,-1]∪[0,1]