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Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 22

Answers (1)

Correct option (a)

Hint: Take two conditions, x<0,x>0 to identify the type of function.


Explanation:It is given that


Case (i):

If x<0

\begin{aligned} &\Rightarrow|x|=-x \\ &\therefore f(x)=\left(\frac{x}{1-x}\right) \end{aligned}

Differentiate (i) w.r.t  x


So, function is increasing.

Case (ii):

If x>0

 \begin{aligned} &\Rightarrow|x|=x \\ &\therefore f(x)=\left(\frac{x}{1+x}\right) \\ &f^{\prime}(x)=\left(\frac{x}{1+x}\right)^{2}>0 \end{aligned}

So, function is increasing .

Hence, the given function is strictly increasing.

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