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

1 Answer
Jul 29, 2018

Answer:

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]}