Function `f(x)=|x|-|x-1|` is monotonically increasing when (a) `x<0` (b) `x >1` (c) `x<1` (d) `0

Explanation

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

for `x>1`
`
f(x)=x-(x-1) `
`=1 `
`f^{prime}(x)=0 `

`Rightarrow 0 lt x lt 1`
` f(x)=x-(1-x) `
`=2 x-1 `
`f^{prime}(x)=2>0`
Monotonically increasing
` Rightarrow` for `x lt 0`
` f(x)=-x-(1-x) `
`=-1 `
`f^{prime}(x)=0`
`
Rightarrow `for `x lt 0`
`
f(x)=-x-(1-x) `
`
=-1`
`
f^{prime}(x)=0`

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