please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16 .1 , question 6 maths textbook solution
is a decreasing function on
.
is increasing on
Hint:
Given:
To prove:
decreases in the interval
and increases in the interval
.
Solution:
Here we have two cases:
Case I: if
Let Such that
Then,
[Squaring on both sides]
[Adding 1 on both sides]
Thus, for all
.
So, is a decreasing function.
Case II: if
Let Such that
Then
[Squaring on both sides]
[Adding 1 on both sides]
Thus, for all
.
So, is increasing function on
.