What is the range of the function $f(x)= abs(x-1) + x-1$ ?

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Answer 1 · 2018-07-29T16:36:11

Range of $|x-1|+x-1$ is $[0,oo)$

If $x-1>0$ then $|x-1|=x-1$ and $|x-1|+x-1=2x-2$

and if $x-1<0$ then $|x-1|=-x+1$ and $|x-1|+x-1=0$

Hence, for values $x<1$ , $|x-1|+x-1=0$ (also for $x-0$ ).

and for $x>1$ , we have $|x-1|+x-1=2x-2$

and hence $|x-1|+x-1$ takes values in the interval $[0,oo)$ and this is the range of $|x-1|+x-1$

graph{|x-1|+x-1 [-10, 10, -5, 5]}

What is the range of the function f(x)= abs(x-1) + x-1f(x)= abs(x-1) + x-1?