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Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 18

Answers (1)

Correct option (d)

Hint: Take 3 conditions  x<0, x>1 \& 0<x<1 and check whether the function is increasing


Explanation:It is given that


Case (i): If x<0

\begin{aligned} &|x|=-x \&|x-1|=-(x-1) \\ &\Rightarrow f(x)=-x+x-1=-1 \\ &\Rightarrow f^{\prime}(x)=0 \end{aligned} 

So, the function is not monotonically increasing when x<0

Case (ii): If x>1


\begin{aligned} &\Rightarrow f(x)=1 \\ &\Rightarrow f^{\prime}(x)=0 \end{aligned} 

Thus,f(x)  is not increasing when  x>1

Case (iii): If 0<x<1

If 0<x<1  then |x|=x \&|x-1|=-(x-1)

\begin{aligned} &\Rightarrow f(x)=x+x-1=2 x-1 \\ &\Rightarrow f^{\prime}(x)=2 \end{aligned} 

So, the function is monotonically increasing when 0<x<1

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