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

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.

Given:f(x)=\frac{x}{1+|x|}

Explanation:It is given that

f(x)=\frac{x}{1+|x|}

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

 f^{\prime}(x)=\left(\frac{x}{1-x}\right)^{2}>0

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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