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Function f(x)=|x|-|x-1| is monotonically...

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

A

`xlt0`

B

`xgt0`

C

`xlt0`

D

`0ltxlt1`

Text Solution

Verified by Experts

The correct Answer is:
4
f(X)=`|x|-|x-1|`
=`{{:(-x-(1-x),xlt0),(x-(1-x),0lexlt1),(x-(x-1),xlt0),(-1,xlt0),(2x-1,0lelt1),(1,xle1):}`

Graph of the function shows t hat f(X) clearly increases ion(0,1)
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CENGAGE PUBLICATION-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
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