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  • please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 8 sub question a maths textbook solution

please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise 16.1 , question 8 sub question a maths textbook solution

Answers (1)

f(x)is strictly increasing in (0,\infty)

Hint:

Use f(x)=|x|=\left\{\begin{array}{l} x, \text { if } x>0 \\ -x, \text { if } x<0 \end{array}\right.

Given:

               f(x)=|x|

To prove:

We have to prove that function f(x)=|x| is strictly increasing in (0,\infty).

Solution:

Let x_{1},x_{2}\in (0,\infty ) and x_{1}>x_{2}

Sincex_{1},x_{2}>0, therefore the function of x_{1},x_{2} is

               f\left(x_{1}\right)>f\left(x_{2}\right)

Thus, x_{1}>x_{2} \Rightarrow f\left(x_{1}\right)>f\left(x_{2}\right) for all x_{1},x_{2}\in (0,\infty ).

So, f(x)is strictly increasing in (0,\infty)

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