x>=a,‌ so ‌|x−a|=x−a x<100,‌ so ‌|x−100|=100−x f(x)=(x−a)+(100−x)+|x−a−50|=100 or, |x−a−50|=a
From the graph we can can see that when x=a then |x−a−50|=a or, a=50 Similarly when x=a+100 |x−a−50|=a or, a=50 So value of a is 50 when f(x) is 100 .