Let I be an interval disjoint from . Prove that the function is strictly increasing on I.

Consider

We can see f’(x) <0 in [-1,1]

i.e. f(x) is decreasing in this interval.

We can see f’(x) >0 in (-∞, -1) ∪(1, ∞)

i.e. f(x) is increasing in this interval.