Question

$f\left(x\right)=|x|-|x-1|$ is monotonically increasing when

• A. $x<0$
• B. $x>1$
• C. $x<1$
• D. $0<$ $x$ $<1$

Answer 1

Answer: (D)

$0<$ $x$ $<1$

$f\left(x\right)=\left|x\right|-|x-1|$

For plotting $f\left(x\right)$ we would need different cases

Case $1:x<0$

$f\left(x\right)=-x+(x-1)$

$f\left(x\right)=-1$

Case $2:x>0$ and $x<1$

$f\left(x\right)=x-(-x+1)$

$f\left(x\right)=2x-1$

Case $3:x>1$

$f\left(x\right)=x-x+1$

$f\left(x\right)=1$

(Image)

Clearly $f\left(x\right)$ is increasing for $xϵ(0,1)$