Question

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

Answer 1

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

Explanation:

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]}