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

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

Given:f(x)=|x|-|x-1|

Explanation:It is given that

f(x)=|x|-|x-1|

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

So,

\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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