Question
Let be any interval disjoint from . Prove that the function given by is strictly increasing in interval disjoint from .
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Text solutionVerified
The points and divide the real line in three disjoint intervals i.e., , and
In interval , it is observed that:
Thus is strictly decreasing on
and on and
is strictly increasing on
Hence, function is strictly increasing in interval disjoint from .
Hence, the given result is proved.
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Question Text | Let be any interval disjoint from . Prove that the function given by is strictly increasing in interval disjoint from . |
Answer Type | Text solution:1 |
Upvotes | 150 |