Question

Let I be any interval disjoint from (−1, 1). Prove that the function f given by

is strictly increasing on I.

Answer 1

We have,

The points x = 1 and x = −1 divide the real line in three disjoint intervals i.e., .

In interval (−1, 1), it is observed that:

∴ f is strictly decreasing on .

In intervals, it is observed that:

∴ f is strictly increasing on.

Hence, function f is strictly increasing in interval I disjoint from (−1, 1).

Hence, the given result is proved.