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Question -

Let I be any interval disjoint from (−1, 1). Prove that thefunction f given by is strictlyincreasing on I.



Answer -

We have,

The points x =1 and x = −1 divide the real line in three disjoint intervalsi.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 strictlyincreasing in interval I disjointfrom (−1, 1).

Hence, the given result is proved.

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